It will also depend on what type of scar you have. I told the doctors when I went in for gall bladder removed that they would not be able to do keyhole surgery. Of course, they tried, so I have those scars as well as the actual scar where they had to cut for conventional surgery, which is still visible after 20 years. I just measured it, it is 19 cm long. I can't remember exactly how long I had to go without bathing, but I reckon it was a good ten days to two weeks before I had the stitches out.
If you had keyhole surgery you can follow the link posted by jaxjacky of course.