Frame of reference.
This was your first bass, and as you've said, it was a cheap, learner instrument.
Now that you know how this instrument feels and sounds, you'll be able to tell how much nicer a better instrument will feel and sound without needing anyone else's advice, because the characteristics of this bass are already in your frame of reference.
I, personally would not put another cent into a starter instrument. I don't believe in saving/improving inexpensive instruments, because after you do this, you'll still want a better instrument sooner or later, and whatever money you sank into the starter bass will not be recovered.
On the other hand, if you like to tinker or would get the feeling of having accomplished something by straightening out this, your first bass, then I'd say go ahead.
When I was younger, I replaced pickups, bridges, nuts, et cetera on some of my basses to try and get the sound I wanted, but nothing equaled the satisfaction of trying and buying a well-made, factory fresh bass that had the sound I liked right off the rack.
I'd even recommend borrowing (a little) money if necessary to get something you know you really like, and be done with it.
That's my advice.
Good luck.
Mike
