How do I refurbish my fibreglass bathtub?

call a glazer.

In my opinion, unless this a special type of tub, I would use it for a garden outside and buy a steel tub {Dreamline has them relatively cheap~ about $200 ~ look online}. No tub refurbishing, unless sent out, is worth the money invested. Many people now have the fiberglass type tubs which are generally more expensive and less environmentally friendly. Longevity between the two types is, in my opinion, hands down in favor of steel. I even seen animal water troughs made out of galvanized steel and set on a rubber pad that angles slightly so the water drains well used as a tub and had a matching smaller piece for the sink. It actually was quite beautiful. A large tub will run you a bit over $100's the angled rubber I have no idea the cost.

Sounds like your tub is degrading fast, I agree replace it. You can also go to an architectural recycler and find a used cast iron tub or steel one.

Fiberglass is a hard one to repair. Keep in mind that a lot of automobiles have fiberglass bumpers or fenders. Try an automotive polishing compound. Talk to the manager at Autozone or automotive supply near you. You'll want something you can use to buff out the scratches and leave polished looking. If you do this, take care in stepping in the tub at first so you don't slip. Use a rubber mat at first for a while.