When trying out bows last year, it was suggested to me to wipe off the strings after rosining. Especially if you're rosining and trying out, comparing between even two or three bows, you will have a hard time keeping the rosin on each at similar amounts and keeping it from building up on the strings by the fourth bow is crucial to being able to tell the difference in each bow's sound. My recommendation is to rosin the bow, then play a light tremolo covering all of the hair (frog and tip) - this will both help spread and warm the rosin and remove the excess rosin that will fly off when playing anyway. Then wipe off the strings (with downward strokes-keeps rosin away from the fingerboard), the top of the bridge and the body of the bass and bow with a cloth you've designated as your rosin cloth. If you wipe everything down again when you are done playing, you will have a much easier job keeping your bass clean. It is my experience that most of the rosin that ends up on you bass and bridge ends up there immediately after rosining and doesn't help you at all in playing. Rosining vigorously will make your bow sticky, but it'll also leave snowflakes all over your gear - that is simply wasted rosin that will end up muting the sound of your strings and, if not cleaned up, damaging the varnish on your bass and bow.
Don't get me wrong, I don't use rosin sparingly in the orchestra - we need a good amount to get the strings going- but don't let the wasted rosin mess up your gear and your sound.