Don't give up! Keep playing with bare fingers until they get a bit sore, then give it a rest. Using the tape is a last resort when you get blisters and want to keep playing.

I'm short too (5'4") and support the bass by leaning the side against my stomach, so it becomes a sort of dancing partner that way, both of us having something to hang onto.

The action (height) of each bass is different and makes a difference in ease of playing, along with type of strings. I would just get used to what you have for awhile before you ask a luthier to vary things.

One thing I don't think anyone mentioned, play the strings (with right hand) down near the end of the fingerboard, rather than up higher on the neck.

Once you get used to things, you'll realize how much FUN and how gratifying it is to play bass.