Thanks for the smile. I can remember my first few falls. Everyone today talks about trainers, but have forgotten rollers. Maybe that's why I'm more careful now, and see poorer handling skills, on training rides than many years ago. The bottom line: Your new rollers are being entirely unforgiving in showing you just how unsmooth you are on a bike. And that's why I said in another thread that when can ride rollers with no hands, you will
NEVER again be accused of not being able to hold a straight line and ride smoothly.
Just keep at it. Please, do not give up. Yes, you'll likely fall a few more times--but I guarantee you there will be falls on the road you will not have, and about which you will never know, because of your much improved riding/handling skills. You'll be completely comfortable fully dressing and undressing on the bike. You'll easily avoid road obstables even while riding with no hands. Balance will become an afterthought. You will become more attuned to your bike [and body] than you now think possible.
But the very coolest thing will be eventually discovering you can ride your rollers with no hands. (But even should you not get there, you will be a much better bike rider.) You'll be so smooth that others will notice a very discernable difference in your riding style--from the time before you rode rollers, and compared to cyclists who never have. People who have never seen you ride will recognize you as a very proficient cyclist. Seriously, your improved form will be that obvious. Look forward to those moments while you're looking at down at that "white line."
One more thing: Start out in a bigger gear than you're probably using now. You'll inherently be smoother at a lower cadence. Pick up your cadence to a normal road spin as you gain ability and confidence.