I would recommend to hone in on timing when you have a complete section or phrase down. You referenced mastering four bars at a time before moving on, that’s perfectly fine. Most songs are written in eight bar phrases, for example: A verse or a chorus. So splitting that in half, is an excellent approach for learning quickly. But I would also recommend to work on the transitions.
So if you master bars 1 through 4, then you master bars 5 through 8, don’t forget to go back and work on bars 4 to 5. I commonly notice people forgetting to work on the transitions. The same would apply when you are playing from one section to another, a verse to a course for example. So you would work on the last bar of the verse to the first bar of the chorus.
Hope that helps!