I did it the other way around. I'm a classically trained pianist who took up bass as an second instrument.
As such, learning another instrument came easy because music is really generic information for all instruments of pitch. The main differences, but not all of course, is the technique required to play it. There is no difference note wise, of a G major seventh chord on Bass as there is on a Tuba. (G major seventh chord consists of a G B D F# )
As for approaching the instrument, the piano is easier because a 2 year old can hit a single key and there is a perfect pitch for that note struck, where as a bass, it takes proper finger tension in the right spot along with a clean pluck to produce the note.
As for learning notes, scales, etc. Bass is easier because Bass has many one pattern fits all keys, not true with pianos. That's why there are so many players who can get by without learning to read music or even know where or what the notes are on the fretboard.
A good example of this is when I read about one of my favorite bass players, Steve Harris, saying how he likes the "odd chord shapes" he plays in one of his songs, when in fact he is playing an augmented chord which nothing more than a major chord with a raised fifth, nothing odd about that.
If all you aspire to do is be a rock-n-roller, you can get by with just working different patterns for licks and play the root of what the guitar player is doing. But that might come back to haunt you someday.
If you aspire to be more than that, there is no substitute for a real teacher who teaches music, not licks and tablature. I would suggest choosing one instrument that holds your desire to play and stick with that before you take on another.
Learning to play another instrument will also give you insight to what musical information you have learned and apply it to another instrument. As far as I know, it is still required at Major music schools to take up another instrument for that reason.
Hope that helps!