PRACTICE... and lots of it
I am purchasing a bass on Friday. I'm always plunking around on them. But i am making it a POINT to sing and play at the SAME TIME from the GET GO while LEARNING how to play the Bass! I HAD the same problem when i taught myself how to play the piano. I could sing and play simple stuff, but when the songs vocal melody and the piano tune were...off or complicated, i'd either start singing the piano part, or playing the vocal part. To correct this problem, i started SPEAKING the vocal part to get the phrasing correct while playing the piano part...when i got that down, i would then HUM the vocal part while playing the piano part, then would break the song down into smaller sections and REPEAT...SLOWLY playing and singing. Then gradually speed up as i got more comfortable with the tune...then move onto the next chunk. It's time consuming and tedious and takes a lot of dedication, but it can be done. I have faith in you. I STILL have to do that with EVERY song that I write or perform and need to sing and play. However. Once you 'GET' the song. You've GOT it, you'd be surprised at how well it 'STICKS' if you use that method or one similar. Plus, the process gets quicker and quicker the more you use it. Good Luck!