I have 3 existing vents through my basement wall in one area of my house and would like to tie my basement Bathroom vent into one of them. Is this legal? I'm trying to avoid another wall/siding penetration. The existing vents are (1) for the cooktop down draft; (1) for my electric dryer; (1) for my propane water heater. Thanks.

Those vents are more like an exhaust stack and you should not tie a plumbing vent into them. Your best plumbing vent would terminate above the roof line but can run exterior of the house but not terminate below a window or doorway.

Also, you may extend the vent into the attic and revent back to a existing roof vent. But Bob's dead on, you can not connect to anything but the roof , a AAV, or another dry vent. Good luck, Tom

No, you cannot connect pluming fixture vent to any of those listed. You need to run new vent all the way through the roof or connect it to existing vent above anti-siphon level on the floor of the particular plumbing fixture this vent vents.