I will be installing self adhesive vinyl square in my bathroom. How do I cut the tile to the contour of the tub for a nice fit?

A contour guide is a tool designed for just this purpose. It has a series of wire fingers that slide in and out of it's housing allowing you to transfer the profile.

Contour gauge QEP Contour Gauge, for Shape Tracing for Accurate Tile Cutting - 10016 at The Home Depot

You can make a sort of one time use contour gauge as well by using a whole bunch of toothpicks or by cutting the loops off paper clips, lay some making or duct tape on the floor, adhesive side up, lay the toothpicks or paper clip wires onto the tape, touching the edge of the tub and place another layer of tape over top. Transfer the profile to the tile you are cutting. Masking tape on the tile and a pencil will allow you to transfer trace the profile more accurately. Once the profile is transferred, scripe a new line about 1/8" in from the exact marking to allow for your caulk joint. If the tile directly touches the tub, it will end up debonding from the floor in time.

U can also use a scribe and make a paper template.

Chuck