Singing and playing is often harder with bass than guitar. IMHO the process is study, analyze, practice, practice, practice. It should get easier as you build repertoire. So I suggest starting with a relatively easy song.
I think one of the things that makes bass harder is you have to deal more with aftertouch...I.E. controlling decay and muting.
The approach I use is to learn each part individually, and then figure out how the parts fit together rhythmically. Playing piano or drums involves a similar approach. With piano you coordinate both hands to play one part. With drums you coordinate both hands and both feet to play one part. When you sing and play, you view it as one composite part and coordinate your voice and both hands. Writing both parts out in a grand staff can help you see how everything fits together. Start slow and out of time, and then work it up.