Collecting rings from bells is not cheating; neither is digging up rings as Knuckles for that matter. It does, however, give rise to a procedure that can be repeated an arbitrary number of times, allowing for a ring total that has no upper boundary apart from the byte cap. This is undesirable, of course.
Some limit needs to be placed on repetitions in order for the chart to be brought back. Using consecutive hits on the bell and not running away, it stops giving rings after the 5th hit, so I used that 5 count as the most reasonable benchmark for a cutoff. This rule was intentionally created to say nothing about what can happen in between those hits, so that optimal use of your 5 can give you an extra 10 rings over straightforward attacking all at once, but so that there's still a limit (not specified explicitly by the rule, but it can be 25 instead of 15).
The 15-ring limit comes about by placing a restriction not on the procedure but on the results thereof; "if you do it this way you can hit the bell 5 times but if you do it a different way you can only use 3"? I'd rather avoid shifting the limiting factor to that end where possible.
The alternative is to choose a number where it doesn't matter whether you count on procedure or results, as the number would be chosen so those would be equivalent. There are two choices for a hit limit that fit the description in this case: 0 and 1. Of these, 1-hit would at least acknowledge the bells' mechanical presence as a source of rings. Pointing out that digging rings are also present mechanically could be a case for 0-hit, but I see a distinction in that the rings given off by a bell hit are completely predictable, unlike the random payoffs from digging, so that it can still be allowed and restricted at the procedural level. Following the precedent of infinitely repeatable, yet predictable, actions such as S3K Act 1 signposts and the Launch Base alarms, placing the cutoff at one repetition seems like a reasonable thing to do, and would let each bell count for 5 rings.
In descending order, my preferences for the limit to be imposed are 5 hits, 1 hit, 0 hits, and 15 rings.
I'm not quite sure what to do about Twinkle Park and Lost World though, because you certainly can't stop people from hitting switches a first time. Perhaps the best option is thus:
If you hit any switch more than once in Twinkle Park or Lost World, your total does not count.
I didn't make the rule that way because it generates both false negatives and false positives. You can stand on a switch while carrying a Lightning Shield, let the rings get sucked in and constantly reappear (or, possibly if the first ring spawns close enough to the switch, you might be able to stand on a point such that the switch remains held down and you also cover up and grab that ring even without the shield, as is possible in the Station Square hotel), and still claim that you only hit the switch once. On the other hand, imagine you're preparing for that part in Lost World, and charge a light attack near the switch. All those energy balls fly around you, and some of them will run into the switch thereby pressing it down. You might hear the sound of the switch multiple times, and if you do, then technically speaking that run would be disqualified--clearly not something that's supposed to happen.
I've made the rule in a way that I believe stops everything that shouldn't be done and nothing more: once you get any of the rings from a switch, you can't generate any more rings from it. Is there anything that needs to be improved from that?