I haven't touched the demo, so I wouldn't know.
The bow is available in Story Mode in the current version, and in Arcade Mode.
The bow is not a primary weapon, so if you were to be a magic or melee user, you can still use it as a viable source of damage since its power scales with level and not stats. (Not to include a hat available in Story Mode) And arrows are limited, but there are plenty to find and pick up while fighting.