Should I wait for Tower to provide runway exit instructions? This is somewhat already answered here (Is it a flight violation to mishear ATC instructions for exiting the runway?), but this question is more geared toward taking action before hearing from Tower.

I fly out of a towered airport somewhat often. 99% of the time when they provide me with a runway exit (Taxiway B in this case), it's the same one.

Sometimes however, they do not provide me an exit instruction quickly enough despite the fact that I'm rolling up to where I should be exiting for Taxiway B. They might either be busy with other aircraft or simply don't call out an exit instruction. Sometimes I've just rolled past Taxiway B and other times I start heading my aircraft in that direction just to finally hear Tower give me instructions to exit via Bravo.

So, the question is, if I know I'm almost always going to be assigned a given taxiway, should I take it or should I always be waiting for Tower to assign one and thus just keep idling down the runway until I get an assignment from them?

This becomes even more important when flying into unfamiliar airports. Do you just keep rolling or do you take a taxiway when you know you can?

I will like to clarify, 100% of the time, I have received a taxiway instruction AFTER I've started to point the nose of my aircraft at a taxiway. I have never actually exited the runway without finally receiving the instruction.
Note: I am assuming you are asking about US regulations.
If the tower does not give you an instruction, you should not wait for one. Leave the runway at the next available taxiway and then wait for further instructions:

4−3−20. Exiting the Runway After Landing
The following procedures must be followed after landing and reaching taxi speed.
a. Exit the runway without delay at the first available taxiway or on a taxiway as instructed by ATC. Pilots must not exit the landing runway onto another runway unless authorized by ATC. At airports with an operating control tower, pilots should not stop or reverse course on the runway without first obtaining ATC approval.
b. Taxi clear of the runway unless otherwise directed by ATC. An aircraft is considered clear of the runway when all parts of the aircraft are past the runway edge and there are no restrictions to its continued movement beyond the runway holding position markings. In the absence of ATC instructions, the pilot is expected to taxi clear of the landing runway by taxiing beyond the runway holding position markings associated with the landing runway, even if that requires the aircraft to protrude into or cross another taxiway or ramp area. Once all parts of the aircraft have crossed the runway holding position markings, the pilot must hold unless further instructions have been issued by ATC.

(Aeronautical Information Manual, emphasis mine)