Is it to be painted or stained? Are you up for a cool woodworking project or do you want something you can nail up in a few hours and paint?
For painted trim, look up "flextrim". It's a polyester resin formed in any curvature and profile you need.
If you want stain grade wood, there's several ways to go, but more time will be required, and to DIY, lots of neat tools to buy!
Casey

Casey, thanks. I would kinda like a DIY project. I don't want to spend a fortune on tools though. Please, feel free to let me know any tips or things I kind do for this? I'm going to be painting it.

I'm looking forward to hearing Casey's approach to this job. Steam-bending of pre-cut moldings seems unlikely, and bent lamination would require an awful lot of equipment for a DIY project. I'm thinking a good bandsaw for cutting lams, and a vac press. Where are you headed, Casey?

You know, I take it back; steam bending may be the way to go. Still, it's a big job. How large a baseboard profile are you thinking of?

Steam bending for braod curves like this is actually pretty easy.
You will probably not even need a back up strap.
A wallpaper steamer is a good source of steam for bending, or a brand new 5 gallon gasoline can and a propane burner.
A section of 'universal' car radiator hose claps over the pour spout, and a correctly chosen weight sits on the upside down screw fill lid.
Steam bending is very low pressure, just enough to get som e flow. Just a few PSI.
The steam box can be made of plywood, or even 2 inch thick foil faced foam insulation.
For basebord you do not even need to hit the bend exactly since the nails will hold the material in place.

In my job I have to come up with solutions that can be done on-site with the stuff we have available. Steam bending is very cool, but it would require a caul (form) other than the walls themselves. What I'm thinking of could use the room as the form. I'd try 1/8" plywood (perhaps 1/4" would bend to 14ft dia. Lumberyards also sell a plywood product made just for this application. It's $40/sheet at my supplier) laminated with glue (titebond II) This could be applied directly to the walls, provided that the surface is uniform with no voids at the base or flat spots. The sections could be held tight to the wall with blocks screwed to the floor. (overlay with plywood to protect existing floor if necessary) If you could get a veneer plywood of the desired species, that would be used as the last lamination to "show". You would want to be able to dress the edges of this glue-up somehow after it dried, so don't glue it to the wall, and use some wax paper on the floor to release the glue, have some egress route planned for the assembly once its dry, or make it a bit longer so it can be cut in two for machining, then reassembled in place (biscuits).
I just did a small curved-top cabinet using 1/8" lauan as the bendy-board. The amazing thing was, unlike with steam bending I've done, there was no spring-back with the ply-laminate.
The room has, what, 38+ feet of base? That's a lot of material to steam bend; brick, what length of steam box would you want to use?
The real problem I've observed w/steam bending is that the middle of the board gets the curve easily- it's the ends that are a beeatch; there's no "leverage" available to help with the bend; for windsor chair arms, there's no problem- their ends are straight anyway, but architectural curves need to be conistent, so there's going to be some waste at the ends of each section.
Bandsawing out solid wood is going to be a tremendous amount of waste, and result in short sections. But it would be the way to go to add a solid border to the top of the base in which to run a moulded edge detail, without exposing plies.
I forgot to mention that flextrim comes in at least two finishes- smooth and wood-grain, so that you could antique/glaze it to bring out the molded grain effect.
In the end, there are also businesses who specialize in curved woodwork, and will be happy to take your money for any molding profile in any wood you want. Disadvantage other than the $$ is lead-time, shipping, potential for mistakes.
Casey

My opinion. Since it will be painted, I would try MDF. First of all, they make MDF with kerfs already sawn in it ready to bend. But before I would try that, I would try bending the solid MDF since it is a relatively shallow curve. You can lean a sheet of MDF against a wall and in a couple of days it will have a bend in it. Be sure you have waxed paper under the molding so nothing sticks to the floor. I don't want to go through the rest of this method if no one is interested. When the company I used to work for made curved stair parts they had bending forms made of pheonlic resin and we would do bent laminations on site, but I don't think that would be applicable here.

"Steam bending is very cool, but it would require a caul (form) other than the walls themselves."

Steam it on site and nail it in place while hot and moist.
If you use duplex nails you can pull them after the wood sets and finish it on sawhorses instead of on hands and knees.

You do not usually need to hit the curve exactly like in furnture making. You can simply bend the wood the last little bit as you install it.

I have made site built steam boxes to hold 16 foot sections of molding.
All it takes is $$.

I think our guy maybe went to another site out of exasperation. But anyhoo, if a person were to want me to do this job, I would use bent lamination making a bending jig (however high, 2", 4", 6", ect.) out of MDF. The success of the job depends on the bending jig. I just made a 3ft high, 2ft wide pirates chest with an extreme parabolic type curved top using this method. I'll try and post sosme pictures if anyone is intrested and I can figure out how to do it.

There are flexible trim moulding products on the market that can help you with this issue without all of the costly jigs or steaming box buildups and additional labor. The flex trim mouldings I have seen used were stained and looked just like their natural oak wood counterparts. They do cost more but require no learning curve in use so the labor time savings help offset the price. It might be worth a look.

Here is a link that might be useful: Flex trim flexible mouldings

That site has already been posted but I think this guy quit reading this days ago.

Here's a quick and easy steamer I saw in an on-line video. They were using it to make sail boats but would work well in this case. Use a piece of 6" pvc pipe and mount screw on caps to each end. In one end drill out a hole for 1/2" copper pipe. Place a steal funnel over a pot of water on a hot plate. Connect the funnel to the pvc with the 1/2" copper tubing. The steam will fill the chamber and in about 20 - 30 minutes you can remove your trim piece from the pvc chamber and bend it any way you want. These guys were making viking sail boats but there's no reason it wouldn't work with trim for a round room.

"Use a piece of 6" pvc pipe and mount screw on caps to each end. "

You have manufactured a pressure vessel, a very bad idea.
All you need to close off the ends of PVC, downspout, or even a wooden box is some foam. Roll it up and stuff it into the end.
There is ZERO pressure involved in steam bending of wood.
The only reason you even put a cover on the stema source is to make sure the steam goes into the box.
A hot plate is a very low power source of heat.
The rule of thumb for steaming time is ~20 minutes per inch of thickness.
The wood must get hot and wet.

"The rule of thumb for steaming time is ~20 minutes per inch of thickness. "

You're sure about that, Brick? The rule I've consistently seen (and used, though only occasionally) is 1 hour per inch.

The screw-on end caps are absolutely a risky idea, but it sounds like the rest of the system Bob described was leaky enough to prevent any pressure buildup.

Lee Valley offers a very good PDF tutorial on steam-bending.

Here is a link that might be useful: Lee Valley steam bending booklet

I used to take a length of metal downspout and fold over one end and flatten it shut. I would prop it up on one end, and put a fire under it. A rag stuffed in the open end kept enough steam in there to do the trick. You need to keep the steambox close to the work, though, The wood loses its flexibility pretty fast. For lazier curves, I just throw the wood in my swimming pool for a day or two, then put it up on some blocking, and weigh down the ends. As someone said, you don't have to be exact. If the room was 14' in diameter, I'd just cut a 2X4 a couple inches shorter than that, and use it to hold the wood in place while it dried. I've steamed a lot of boat ribs; I don't remember how long- you learn from experience when they've cooked enough.