Well, it's helpful that 1-20 correlate a little between 3.x/PF and 5E than 4E.
I'd say, BAB/4 (round up) + 1. Level 1 BAB +1 => +2 prof, and Level 20 BAB +20 => +6 prof, with a linear progression.
EDIT: My apologies, you are talking about total attack bonus, not base attack bonus. Back to the...