Get your own parts what that shop is doing is making you buy the entire hub and charging you the same labor charge as it would to press it in and out. I paid 125 for labor +25 for the bearing. When you work 7 days a week it's easier to just pay someone to do it
It's not a difficult service if you have the tools. Your worst enemy is definitely rusted nuts and bolts. And yes do both at once. The first time you do this yourself it will probably take 2 hours or so. Just make sure you have the time and tools or take it somewhere. I recommend timken/koyo bearings personally.
If you don't have a press this will not be an easy job. Get a second opinion on the price but $250 is about right for a shop to do these bearings. I would not go with a cheap bearing like Timken, use SKF or Mazda Bearings. Proteges are notorious bearing haters because of the way the engineers made the hub assembly with the drain slot. Do not buy the seal or have them installed with the new bearings. Mazda actually had them removed because of crap getting caught between the bearing and the seal because of that bastard drain hole that actually killed the bearings. This is all my own opinion and I have a full shop to do this work in and it was still a pain in the ass.
Well then. I didn't consider timken being a cheap bearing. You must remember that they were recently bought out by Koyo.