Law Stack Exchange could surely help you from a consumer law perspective. The New York Times’ ethicist column or similar could also advise. However, from a cycling perspective, I would expect a bike shop to know the relative value of the bicycle compared to what it would take to get it running. I would expect them to call the consumer if the bike was going to take a lot more work or cost a lot more than expected. I believe this is a common expectation. They definitely failed on this score.
If the bike were sitting outside for a year, then unfortunately, the amount of damage described is plausible. The seatpost and the BB being seized is expected. I would actually expect anything with bearings plus the chain to be badly damaged and possibly uneconomical to just service, meaning that the headset was probably also involved. I would assume all cables and housing needed replacement. Furthermore, the frame might have internal rust, which can cause a frame failure if it’s bad enough. Continuous exposure to wet weather is truly evil. Thus, we always counsel strongly against simply leaving a bike outside. They aren’t cars. If we built bikes to be as weatherproof as cars are, they would weigh a lot more and would be a lot less fun to ride!
A reasonable mechanic should know that an average Trek road bike from the 1990s isn’t objectively that valuable. I wonder if you heard correctly that they absolutely needed to get a $250 replacement square taper BB, but if so, that should objectively have raised a red flag with the mechanic to call the customer. I’ve not worked in a bike store, but 12 hours of labor does sound like a lot. If the mechanic realized the bike needed that long, they should once again have checked in. If you didn’t tell them the bike was stored outside for a long time, you should have, but that doesn’t excuse their failure. An experienced mechanic should have inferred the general condition of the bike if they disassembled one of the hubs.
As a counterpoint, watch this vid from Berm Peak Express. This was a prank, but he had a fake customer bring a top of the line SRAM wireless MTB group to get installed on a very cheap (I think department store quality, but definitely very dated suspension design) bike. The mechanic said he would check for compatibility, and call the customer. He did exactly that after seeing that the components were indeed compatible, and also asked about some other minor jobs that the bike could use. And this did involve a judgment of economic value, because the chain alone retailed for about what you paid for your bike. Hence, a shop should have called. I believe similar norms operate in automobile repair shops.
It definitely wouldn’t be nice to abandon the bike, but I expect a lot of people in this situation wouldn’t pick the bike up. Surely the shop would have thought about this?? I don’t know the exact legal issues, but there is a branch of law dealing with property abandoned at a business by customers. The shop may be required to retain the property for a short time, but eventually they could probably sell the bicycle if they can (but it’s unlikely they would get back $850). I am not sure what you owe the shop ethically, and I didn’t initially discuss it. Bike shops run on tight margins. I endorse the other answers saying that you should talk to the manager; I argue this was a significant failure on their part. I think it is not ethically optimal to simply walk away, but if the events were correctly described, the shop does need to be informed that they didn’t handle this well. Your leverage is that you can walk away and be out $100.
One thing I really get hung up on is the $250 ceramic BB. This places the BB in premium pricing territory, of the sort you’d put on a top end bike. There are a whole bunch of cheap but perfectly durable square taper BBs from Shimano or from less known manufacturers. (Previously, I made an assertion about Phil Wood BBs, which are a very well-regarded premium option, being considerably cheaper. Phil’s prices have come up since I last remembered, but they are still somewhat cheaper; the steel spindle standard bearing versions are about US$175, plus you buy the cups separately.) Naturally, if you actually want a ceramic BB for your older Trek, you should not let social convention stop you. But again, it was an objectively strange choice to make on behalf of the customer.