I think it is a case of practising I am currently teaching my girlfriend to play bass, and she is having the same issue, as she has small hands. When she first started she couldn't stretch from the 5th fret to the 7th fret using her index and little fingers, but now she can comfortably do it without thinking.
Although, if after a while you find yourself really struggling, there is always the option of getting a short scale bass like a squier mustang and jaguar, which will be easier on your hands.