Sounds like the neck may have too much relief. If you aren't comfortable making truss rod adjustments I'd take it to a local tech for a setup. If you are comfortable making the adjustments then you can tighten the rod about 1/4 turn (depending on how difficult it is to turn) and see if the strings get closer to the board. When you press the E string at the first fret and then at the last fret, how much room is in the center between the bass string and the 12th fret?
