Properly Cleaning an Acrylic/Fiberglass Tub

All my life I’ve had porcelain and/or iron bathtubs that I scrubbed viciously with abrasives like Comet to clean them.

So now we’ve moved into our new condo and I have an acrylic (maybe fiberglass) jacuzzi tub, seven jets, really nice. However, beyond getting the initial grime off with like “Lysol Tub and Tile Cleaner” it seems to HOLD odor and the bottom is INSTANTLY grimy after taking only one bath. Whenever I start filling the tub, it instantly fills the room with that sort of ‘old musty laundry’ smell, and I hate it.

Is there a secret to cleaning these things? And also, should I run the jets with some bleach or something to clean those out or will it damage the mechanism?