Sounds like you are tearing out the existing tub/shower? Destruction could go fairly quickly, but it really depends on how much clearance there is to do things and how open it is.
If the existing pipe is left, as long as there's no water running through it, it should not sweat. But, if you don't cut at least some of it out of the way, you may have real trouble getting the new stuff in where you want it. Plus, you'd need to drill more holes to make room for the new runs, which you may not want to do.
A good plumber can get a feel for what is required, but until all of the walls and areas are opened, it is just a guess. Depending on how willing he is to accept risk, he may not want to give a fixed price, or if he does, it may be high to account for what he hopes it he worst case. There are benefits and disadvantages to doing both time and materials, or fixed price for both the owner and the worker. There isn't as big an incentive to be efficient on a time and materials contract, but it is possible you might end up with shortcuts with a fixed price - it depends on the skill and integrity of the person doing the job. If everything works out well with no problems, a time and materials contract could be less expensive than a fixed price contract...many people prefer a fixed price so they can budget.
I'd get another quote to try to evaluate the likely scope of the job, then decide.
If you can afford to be without the bathroom for awhile, you might get a better quote if they could see what's going on - tear out some stuff like the walls so they can see what's actually there. While you are at it, deal with the drains as well if they include any galvanized, or if cast iron that's not in good shape. It would be a pain to put in a new bathroom, then have to tear things out to fix leaking drains.
Often, you can't evaluate what's needed until you start destruction.