I have replaced the drywall in my bathroom and I retained the old ceiling that has texture on it. My question is what is the best way to tape and mud the wall to the ceiling with texture, do I scrape off some or all of the texture? And what is the best way to do that?

Just tape the edge of the drywall where it meets the ceiling. Keep a nice edge and don't get into the texture ceiling, Tape doesn't always have to fold into the ceiling like that, Another way around this is some small crown molding and hide that joint area. Still mud to ceiling and seal that area.

If you have a pretty tight fit with the new drywall to the ceiling you can finger some spackle to finish filling the gap.When this is dry, wet sand the inside corner,then fill with a GOOD painters caulk,prime and paint.