When someone is "sitting on his/her ass", or the non-vulgar version "sitting on his/her butt", it is an idiom meaning to be lazy or unmotivated.
Related: Someone angry at someone being lazy may then ask them to "move their ass" or "move their butt", or "get your butt moving."
Let me get my ass up and head to the gym.
This means the speaker is recognizing or acknowledging themselves as being lazy or unmotivated, but is forcing themselves to break free of the laziness or acquire the necessary motivation to proceed.
It doesn't mean to hurry. It can imply that the person is in a comfortable state, such as tucked in bed or otherwise relaxing.