Plumbing/venting outside of studs

Do you have any high powered magnets? like the rare earth neodynium magnets? If so you can probably rub one around the wall until it attaches to one of the nails in the studs. Or you can try thumping on the wall, a stud will sound alot less hollow versus empty drywall. That's how I've searched around in the past.

Why do you need to replace the stud? Unless it has rotted, you do not need to replace a stud with water damage. Removed the damaged drywall and any other wet items and let the wood dry out before replacing the drywall.

If this is inside the bathroom, be sure you are using the right type of product. You would not use regular drywall in a shower or bath area, you would use cement board or something similar.