You need to tell the whole story.
Who owns the "bathroom next door"?
Is this a condo or multi occupancy building?

Sorry...didn't realize it wouldn't be clear! I own the bathroom next door. This is a three story row house. I am contemplating turning a small bedroom on the third story into a kitchenette, in order to make the entire third story a more-or-less independent mother-in-law suite. That small bedroom shares a common wall with the bathroom...the wall that happens to be the one with all the bathroom plumbing in it. So I thought it might be a "relatively" easy job to put a sink in to the bedroom. That plus a small refrigerator, smart oven and an induction burner or two and voila...kitchenette!

Knowing nothing about plumbing, however, I'm not clear if one can simply tap into the water supply lines for the bathroom and tie into the drain lines for bathtub or bathroom sink or if a kitchen sink needs its own supply and drain all the way from the basement up.

Thank you.
There can be a number of "affecting" proprietary interests.

What you are proposing can be accomplished. The hot and cold water is pretty straight forward, however, the drain line needs to be carefully selected, in size as well as where in its run you intend to tie-in.
If there is a 3" or 4" stack easily accessible, that would be a good place.

your answer is yes.

As said the hot and cold water are easy to tap off the nearest pipes. The trouble is usually the drain (and related vent pipe) The drain pipe MUST flow down hill all the time at a minimum slope or be vertical. Routing such a pipe can take some creative thinking or serious work. Then comes the vent line.....

A licensed plumber can tell you soon as they see it.