I am planning out my life in Germany, and it will be needed that I travel between a few states in the beginning. Hence, this question arised, would my bank be tied to the anmeldung I gave for it? If so, would I have to change the address with bank everytime I move? Thanks.
You can change address with your bank when you move. However, if you just temporarily reside elsewhere, you wouldn't be moving. You need to have an address of permanent residency in Germany, which is where you are registered and where the bank will send you mail.
Note that some banks only operate regionally. In particular, Sparkasse is often linked to a Kreis (county) or Kreisfreie Stadt (county-free city). If you move to another county, you won't have any offices nearby.