I don't have that independence in my brain.
Can you walk and chew gum?
The reason to compare the timing of the bass line and vocals is to learn to put them together so singing and playing is one composite task; rather than two separate tasks. It takes a lot of effort to put the two parts together. However, it get's easier and easier as you learn more and more songs.
It's helpful to master each part before trying to combine them.
Also, I would suggest starting with songs that are easier.
The complete process might look something like this.
1. Master each part separately.
2. Write out both parts so you can see how they fit together.
3. Slow down and learn to do both parts at the same. You have probably heard the joke:
How do you eat an elephant? One bite at a time. Use the same approach to learn to sing and play. You may have to repeatedly work on one measure or even just one beat.
4. Simplify as needed. This sometimes involves working out a compromise with other players and singers.
5. Practice till it becomes automatic. When possible, it's a good idea to be able to sing/play faster than performance tempo. It could take a couple of weeks....or longer.
6. Learn new songs.
7. Review the songs you have previously mastered to maintain proficiency.