You can start knitting with the white and weave in the end later, but this can leave a small hole, which you wouldn't want in a bikini.
What I do is kind of hard to explain, but I'll try. A few stitches before the color change, start weaving in the end of the white yarn by inserting your needle to work the red stitch, then put the white yarn over the right needle tip from back to front--counter clockwise--wrap the red, remove the white and finish the red stitch. This should catch the white yarn. It has to come up from under the red to work, though, so you may have to play with it a bit.
Do it for a few stitches before and you won't have to worry about weaving in the end later.