Simple raw movement (up, down, right, left) should work. Player movement should be fast and snappy to dodge bullets, but not too fast that the player runs into bullets unintentionally.
Using space or some other key for dashing is also common in bullet hells, you don't have to use dashing if you dont want to. If you do use dashing make it quick and snappy.
Overall bullet hells have pretty simple movement systems, just adjust the variables so that they feel comfortable.