Yes it will get better. I was on 5 mg and had the same feelings you are having. I have slightly high BP, not really enough for meds but I also have PVC's which was the main reason for going on it. I also had slow heart rate at first and felt a bit out of it but after a short while it got much better to the point it does not feel like I am on anything. The big thing I notice is when I run my heart rate stays below 120 when before the meds it would go to 140 on average and if I pushed i can go to 160bpm. When I run I feel normal even at a slower heart rate then before. I actually feel much better. Stick it out and you will do better. Reading the forums I think people give up too fast because they feel weird taking the meds and you really have to give your body a chance to adjust!!
I almost gave up on bystolic when I first started taking it because I felt pretty bad. But I stuck it out for about a month and started feeling much better. Now I can't tell I'm taking anything, it works much better than the atenolol I was taking. I have high/normal blood pressure and it took it a while to take it down. I would try to hang in there.
I do not have any experience with Bystolic, but I have considerable experience with beta blockers. It is my experience with them that after a few weeks the side effects become less noticeable. In my case I had to opposite problem, I take BB to lower my HR, not my BP, but the BP went down too, and it made me prone to dizziness. This passed and now my BP is about normal. I suppose that could be your case with a too low HR, but I do not have any direct evidence..