So, I am no expert, however I have had my struggles with sanding as well.
Two things:
1. Is it essential that you start at 80 grit? Or even 120?
2. Are you only sanding with the lathe on, leaving scratches around the piece as a result?
If your tooling is good enough, especially if you are doing things like proper sheer scraping on the outside, and cleanup on the inside with a good quality and properly sharpened scraper, then starting at 80 grit could BE THE problem. If you end up with a nice clean wood surface, 80 grit is like dragging a newborn baby across a gravel street by horse.... In otherwords, and atrocity to the wood!

If you are tooling to a good finish, then maybe start at a higher grit. Even 120 might still be too coarse, so you might try 220. If you are not tooling your wood to a quality surface, and are instead using sandpaper as a means to say clean up tearout...then maybe consider honing your skill with tools to produce a cleaner surface to start with. Sheer scraping on the outside can do a nice job to clean up quite a bit of tearout on the outside of a bowl, while a good quality scraper can do wonders on the inside. If you generally get a LOT of tearout, I'd look to sharpening your tools more often and better. This was the greatest realization I had when I first started turning...just how important REALLY sharp tools are. Especially with woods that are prone to tearout, a super sharp tool will still cut the fibers and leave minimal if any tearout.
Another thought is if you are only ever sanding lathe-on. This forces the grit to dig in around the piece, which is rarely really with the grain. It may be with the grain at only moments, then cross-grain everywhere else. I always hand-sand my pieces for the last couple of grits at the very least. If you sand only with the lathe on, then your always going to have scratches. TECHNICALLY speaking, you always have scratches no matter what, really. Even at very high grits...its just that the scratches get small enough to become invisible to the naked eye. Up to 400 grit, they can definitely still be visible to the naked eye...and there is potentially another issue with grits that high that I'll get into in a moment. Getting your scratches to disappear, has a lot to do with grain alignment. Sand across the grain, you rip and shred those fibers. Sand with the grain, and you will kind of hide the scratches within the fibers. It can depend on the wood, exactly which aspect of the grain you sand with. There are actually various characteristics in each wood, and some are better at hiding scratches than others. Sometimes, it may just be as simple as sanding the bowl from center to edge along the long grain (which can't be done with the lathe on at all.) Other times, you may need to sand with the aspect of the grain that kind of curves along the bowl from end grain to end grain, which can be trickier, but if you can do it, then you CAN hide the sanding scratches within the grain (well, technically, I guess the proper term for those bands would really be the tree rings.) It really depends on the nature of the wood, though, and what hides scratches best.
On grits...I used to sand to very high grit, as I often used friction polishes for my finish, and t hey seem to work better when you sand the wood VERY smooth. Something I learned somewhere along the way, though, is that beyond a certain point, you are less sanding and more burnishing, with higher grits. Those grits can start around 400 or 600, and the issue gets more pronounced the finer you go. What I noticed in my own work, was that even though the wood surface was becoming VERY smooth, even shiny, despite the grit being very fine, when it left scratches (say counter to some aspect of the grain, which is worse around knots, figure, and other grain oddities), they stood out that much better against the otherwise polished, burnished and shiny smooth other wood. So it may be worth, taking your sanding up to only 320 grit. Then, if you need to sand and polish it even finer, add a sanding sealer, then sand that smooth with a higher grit (600, maybe even 800), maybe put on a couple of coats of the sanding sealer and sand it all super smooth, then put your final finish on. The sanding sealer will help a lot with higher grit sanding (although its definitely not immune to this problem I just described!)