Other than the fact that they're visually similar, guitar and bass are completely different animals with completely different functions. In fact, "bass guitar" is a misnomer, since a bass is not a guitar at all. It's a portable version of an upright bass and it's part of the rhythm section.
A bass should be played as support to the drummer, since it's a rhythm instrument. Bassists usually follow the beat of the bass drum, adding melodic rhythm to the percussion. Most guitarists make the mistake of playing bass like it's a four-stringed guitar, which results in aural chaos. They play too many notes and operate independent of the drummer, so the sound winds up being cluttered and unpleasant. But if a guitarist understands that the bass should not supply its own separate melody, he should be able to make the transition. It's about learning to follow the drummer, rather than the melody.
Physically, you shouldn't have much trouble transitioning from guitar to bass since the instruments feel similar. The additional pressure you'll need to fret bass strings will be offset by the fatness of the strings (much easier on the fingers than guitar strings). And your bass lines will come from the root notes of the chords being played on guitar, so crafting your own bass lines should seem very easy for you.
If you make it a point to single out bass lines when you're listening to music, you'll have a good feel for the function bass serves. It's about finding a groove with the drummer, settling into it, and adding a little melody that compliments the song. As long as you embrace your role in the rhythm section (as unglamorous as it is), you should be fine.