Pulse rate rest at rest of 45 /min is not alarming. However there are several other drugs which are very effective and do not alter the pulse rate. These belong to the groups of ACE inhibitors, calcium blockers and diuretics. I am sure your treating doctor can choose an appropriate medicine which keeps your BP close to 120/80 at rest.
Besides that, I do hope you are on a cholesterol medication and aspirin. If not get in touch with your doctor. It is recommended that these drugs be taken in appropriate dose by all persons who need BP medication. They go a long way to prevent cardiac problems and strokes, etc.
Physical activities are very good and please continue them. In addition, low salt and low calorie diet also is important.