I have never gone in via the ring puzzle. I hate puzzles! Swimming in, alas, creates a problem due to RT; you could in theory emerge in the midst of a bunch of critters while stuck in 10 seconds of RT. I'd suggest 40 ranks of swimming, although the RT seems a bit random, and you can end up with anywhere from 1 to 8 seconds RT even with that much swimming. In fact I once ended up failing the swim totally and getting a chest wound even with 70 ranks of swimming, although that is rather rare and probably requires failing your swim check by a nasty open roll. But that's no big deal, just be sure to carry basal moss for the cure.
As for the critters, there is a place in the NE of the map where you will initially find only krynches and lesser elementals, BUT older critters will eventually find their way in there and then you will be ducking elders and jarls; you may want to ring out when that happens (you can't ring/fog into the Bowels but you can ring/fog out).
The bells of Hell
go ting-a-ling-a-ling
for you but not for me