My doctor just upped my nebivolol dose. my bloodpressure is good by my heart rate is 51 at night. is this normal?

If at night you mean in bed, you'll be fine with that rate. 50 or less when you're up& about is too low. I'm not a fan of using cardioselective beta blockers as first line treatment of hypertension unless you tend to have a fast resting heart rate. I prefer ACE inhibitors, ARB's or calcium channel blockers as first line. & mild doses of diuretics or beta blockers as add ons