I am suspecting bad wheel bearings. I purchased the T/A last winter and I have no idea when the bearings were replaced last, probably never.

The car has a humming/vibrating noise that starts at about 65mph then gets louder as the car continues accelerating. I do not notice anything else, maybe a little shimmy feeling on the steering wheel also. Is this a sign of a wheel bearing problem or something else (alignment?). Car does this on different kinds of pavement and the tires are new.

R-
Chuck

 

That noise can also come from the rear. Do you hear it coming from the front? Jack the car up and spin the wheel. You can tell if the bearings are bad if it is not smooth.
You could also rock the wheel back and forth to see if it has excess play while it is jacked up.
Either way - if you have any doubt, change them. They are relatively inexpensive and not that hard to change. Just make sure you pack them properly with grease or you will be changing them again soon.