Not sure how much they are these days.... but I recommend an Ibanez ATK series bass... should fit within your price range Played with a few before and I quite like them, great sounding and feels good too
If you look around and find an old MIJ JV Squier I think that would be ideal. They've got Mojo to spare and I picked mine up for 2 bills out the door. The back story is Fender partnered with Japanese Manufacturer Fuji-Gen Gakki who at the time was making lawsuit versions of Fender (among other) instruments. Fender decided that instead of battling them they would partner with them. Initially Squier was a Japanese high quality alternative to Fender American instruments, not the entry level brand it is today. You could say that Squier was the precursor to the Fender MIJ/CIJ line. At any rate I have a JV Squier Jazz and again I paid a little over $2oo bucks for it out of a pawn shop. It plays and sounds every bit as good as any American Standard I've laid hands on.
The finishes are a thin poly unlike the thick poly encasing the put on the things now. They age really nicely. Mine has some dings that go all the way to the wood and I really don't care. The PG has a nice aged yellow tint to it and the neck has also yellowed nicely. I do need to take some steel wool to the neck and satin out that finish.