You should have your popcorn ceiling tested for asbestos. Ours had it and it is from the late 70s. They were using this into the 1980s; see link. Our state requires full decontamination (a shower station was put up in our backyard) for all workers and multiple safety regs for it. If your ceiling doesn't have asbestos, it's no big deal. Do it yourself or hire it. It is far easier to remove if someone has not come along and painted over it. If it does contain asbestos, you really need to think twice about doing it yourself. A papermask is not going to cut it! We had contractors offer to remove it for us "under the table" but we didn't want any floating around to breathe later. We also wanted paperwork showing we'd removed it properly if we ever sell the home. One thing we did that we regretted was have the same company do the retexturing and painting as did the decontam. Their painting subs were nothing amazing and I think charged a lot more because they were with the removal people. They have to put two layers of plastic up and they take the first one down after the asbestos is out. Have them leave the 2nd layer up for your own contractors and you'd be happier. Here is a link that might be useful: asbestos Q&A

Nice job of removing the acoustic! Trying to get a smooth finish on drywall is tough because the paper is more porous than the mud joints and will show no matter how finely feathered the edges. One way is to size the entire surface lightly by applying your mud, but wiping off as much as possible. This is similar to skim coating with the exception that you are not leaving a thin layer of mud to try and get an even surface. This is best accomplished with skim coating plaster over blue board.The advantage that you have ,however, is that your ceiling is already somewhat sized because of the acoustic being sprayed on. Even though you have removed the texture, the mud base of the acoustic is still on and adhered to the dry wall. You might give it a go yourself by filling any imperfections, sanding smooth the entire surface.Any bare drywall spots that might present their self you can size as explained. Start with a small area of the cieling and see how you feel about it.If you have the confidence, move ahead. If not, get a pro.

We had popcorn ceilings removed from our 1500 square foot house in 1991 when we bought it and before we moved in. It was a very messy job, but it was done right. We have smooth ceilings and, with the exception just a few inconspicuous areas, no patching had to be done. If your popcorn removal left a smooth celing that's got a lot of cracks and bumps, you will need to patch it up. It can be done DIY, but it's very hard a tedious. The alternative is to hire a professional plasterer, which can be expensive. A less expensive alternative is to hire a handyman who can do a reasonably good job of it, it you're lucky enough to find such a person. One consideration is how visible are the imperfections. That depends to some extent on the shininess of the paint. Flat paint will show imperfections a lot less than shiny paint. But for a bathroom, you'll probably want semi-gloss.

And for those who haven't done this yet, have a small sample tested for asbestos before you do this. Here is a link that might be useful: Popcorn ceilings