The same way people read piano scores that have 2 clefs that are being played at the same time: You practice and practice and you'll get there.
At first, it is hard for everyone to follow two different things simultaneously (in your case, a bass line and lyrics), but if you keep doing it, you'll be able to follow both the lyrics and the music without losing it.
If you find one of those parts easier to memorize than the other, memorize it and follow/read the other one when you sing. That way you won't have to read two things at the same time.
You can also practice them separately. If one of the lines is hard to be read while you sing, practice each one of them separately and then when you feel comfortable with them, put them together, it'll be easier.