Exposing cows to a bull after calving is a management technique that will actually help initiate estrous cycles after calving (shorten the postpartum interval). Bull exposure is not a replacement for a good nutrition program, especially for first calvers. Leaving the bull with the cows doesn't hurt anything. What will likely happen is the next calving season will be longer than if you had had a defined breeding season. If you don't want a long calving season, work with your veterinarian to have him or her pregnancy check and cull those that don't fit into your calving season. Getting cows pregnant with their second calf is a challenge. Having an extended breeding season would likely increase the pregnancy rate of this group of females.
Your question also indicates that you will use one bull to breed these females. If you are going to have a single sire pasture, make sure that the bull has had a BSE (breeding soundness evaluation). Also, check the bull daily during the breeding season to make sure he doesn't get hurt and remains healthy, in addition to servicing the cows that are in heat.
