I pretty much agree with what's been said already - it's probably leaking somewhere in the drain plumbing.
There's a chance it could be leaking from the fresh water (hot and cold water) plumbing somewhere. @JD Martin 's suggested test of filling up a pot (or a bucket) somewhere else in the house, and then dumping the water down the tub drain, will help in finding that. Try to put at least a couple of gallons down the tub drain if you do that; if you have two people, it may help to have one person dumping water down the tub drain, and you on the other side of the wall watching the pipes. If you see water leaking out of the drain pipes when doing this, then it's definitely the drain.
You can also test it the other way if you have a bucket - hopefully at least a 2 gallon bucket, and 5 if it will fit under the tub spout. Put the bucket under the tub spout and turn on the water - the bucket will catch the water so it doesn't go down the tub drain. Then go watch the pipes. If you see leaking water, then the supply pipes are leaking. If it's OK when running the tub spout, dump the bucket someplace else in the house (like the kitchen), and then put the bucket under the shower head. A stepladder might help, and remember that if you have a 5-gallon bucket, it will weigh about 40 pounds when full of water. Turn on the shower, let it spray into the bucket, and go watch the pipes some more. Again, if you see leaking water, then the supply pipes are leaking.
The reason I mention the supply pipe side is because I've seen it a couple of times. Once was with a tub/shower with a single-handle faucet, and it was leaking out of the body of the faucet; the fix in that case was that a plumber replaced the faucet. The other was in a tub/shower where the owner had installed one of those hand shower heads on the end of a flexible hose, with a T piece connecting the flexible hose to the existing shower head and pipe. The tub was over the garage - one day the owner took a shower right before going somewhere in the car, and noticed water on the garage floor. I went over, fearing expensive things, but discovered that the T-piece for the hand shower was leaking like mad. When the shower was on, water was squirting out of the T-piece, hitting the tile inside the shower, running down the wall, through the holes in the tile and wall for the hot, cold, and diverter knobs, dripping down the inside of the wall, coming out around the opening in the floor for the drain plumbing, and dripping into the garage. A new hand shower head with hose and T-piece fixed it for $20.
Whether it's the supply or the drain, get mentally ready for having a hole in the wall somewhere, or a bigger hole than the access panel that is there now - probably in the bedroom that you mentioned is behind the tub. You can get ready-made plastic access panels to cover up the hole, or roll your own with a piece of drywall. Maybe you always wanted one of those full-length mirrors in that spot on the bedroom wall, so you can cover up the access panel later. :)
As far as staying or backing out, that kind of depends on what the plumber says. If it's a few hundred bucks, smile and pay the plumber nicely to fix it and enjoy your new house. If it's a few thousand bucks or more, then you may want to have a conversation with the seller. In between, it's up to you.
(I'm here because @Jim K. pinged me. "I told you never to call me on this wall! It's an unlisted wall." :D )