A bull needs to be with the herd for a minimum of 30 days (not all cows might get bred/settled in that length of time) and for as long after that that you want to spend calving cows. Some farms leave the bull in all year.
I don't believe in doing that. "Most" producers that have a calving "season" like it to be 45 to 60 days. A bull is usually turned out with the cowherd about 30 days after the last cow calved and left with them for the 45-60 days.
If you want a May 1 to June 30th calving, you would put the bull out about 7-22 to 9-20. Then if you use the same dates each year, your cows should have had enough time to be cycling after calving, but shouldn't have to worry about the bull breeding the heifers born that season.