Nobody can give you an answer because there are too many variables that only you can know.
What kind of soil do you have? Sand is going to need water more often. Clay is going to need less water but it needs to be applied with a lower rate emitter.
How big are your roses? Minis versus climbers...take different amounts.
What's your weather going to be? Overcast and high humidity with lower temperatures will take a lot less water that bright sunlight, low humidity, and high temperatures.

Do you know how to snap off a spent bloom at the abscission layer? That's one way to tell if that particular rose is getting enough water.

Do you know to put an emitter head in a bucket to see how much water it really delivers (as opposed to what it says it delivers)?

Where to start? An inch a week. Four days later check the soil and see if it's moist or dry. Adjust accordingly.

While Ann is correct on all the variables, I have 400 roses on drip and I go by rule of thumb. Ideally, bands and minis get half-gallon emitters, 1-3 gal get 1-gal, and the big guys get 2-gal. But half the time I am out of 1/2 and 2 (because I dont get as many, so most end up on 1-gal. I run it once a week for an hour unless the temps are in the high 80s or worse with no rain, and then I up it to every 3rd or 4th day for 45 minutes. Some could use, more some could use less, but nobody dies.

As cats says, you go by the size of your drippers. A 1 gallon dripper should deliver roughly 1 gallon per hour. It doesn't hurt to dig a hole and put a bucket in there under a dripper or two and see what you actually get.

I've found it better to give each rose more than 1 dripper, three is better than two. If one clogs up, you've got the others as a margin of safety, and moisture is better distributed around the root zone with multiple drippers. Just one can leave a dry spot on the far side of the plant.

Your soil is also a factor. Sandy fast draining soil needs more frequent irrigation. Heavy clay that holds moisture well and is thickly mulched may need only weekly watering even in hot weather.

Start off by guesstimating, then for the first season stick your fingers around to feel how moist the soil is, observe your roses carefully, and adjust as necessary.

The newer style dripper hose with the drippers built in every six or twelve inches are resistant to the clogging common in the old style hose. I highly recommend them. They are designed to have some kind of turbulence in the line so that the particles that cause clogs remain suspended in the water, and do not settle out and cause the clogging.

I guess I'm surprised that a garden in Virginia would need irrigation. Here in California we do because in normal summers, we get no rain at all. (All bets are off for this summer.) Roses do like a lot of water, but deeply watered, deeply rooted roses can go several weeks without water if they must. For once-in-a-while watering, I would probably just drag around a hose and a sprayer. Drip irrigation does need yearly maintenance and repair, and you install the supply lines underground so it is not trivial to install.

Rosefolly

Thank you - the above is all very helpful.
Soil is clay, it will be above ground but under mulch.
We have had record breaking heat again today, so having this and being able to be inside in the a/c while the roses are being watered will really help.
If I install 2 of the 1 gph on either side of the plant, will that cut the watering time in half?