By all means pick up the bass if it interests you, it's a highly enjoyable and very underrated instrument. But keep in mind, as the others have said, that it's not just a big guitar with four strings and a longer neck. It's a different instrument that requires different techniques and a hugely different approach to rhythm, dynamics and phrasing. IMHO to play bass well is to think about music in a more structural, groove-based way. It ain't rhythm guitar, let alone lead - there are jaw-droppingly good guitarists who don't know the first thing about bass. It does help, however, that as a guitarist, you already know your way around the fretboard. My advice is get yourself an introductory lesson, and a book or two on bass playing to help carry you through to proficiency. Have fun with it, it's an instrument that you can get a lot out of. In my experience, it is indeed difficult to juggle bass and guitar simultaneously. If you're really heavily into guitar at the moment, stick at it for a while longer, and have a crack at bass when you next feel like it. If you're a bit bored by guitar, perhaps pick up the bass sooner. Either way, as different as they are, you will learn things from bass that you can apply to guitar.

As for the fingers vs. picks debate - I fingerpick the guitar as well as the bass, so fingers are my personal preference, but I think that bass played with a pick can sound just as good. Depends on the style of music, as well. Picks are definitely more at home in metal (although they're not exclusively used - see Steve Harris, Cliff Burton, Geezer Butler et al!), but I've seen them used for blues and even funk as well.