Previous post explains how to determine a safe depth for a given breathing mix in relation to CNS Oxygen Toxicity, only one of the factors that must be weighed when making dives in the range that this is an issue.
Other factors to put into play include SAC and gas narcosis. If your buddy is relatively efficient with his air, breathing an RMV of 12-15 l/min, diving to 55 on an AL80 on a multilevel dive is feasible and safe. Do the math yourself before making these dives.
Narcosis, at these depth, does not impair most divers if conditions are good (no/light current, clear, warm waters). As conditions deteriorate, narcosis becomes stronger and (in some cases) more dangerous. Though if conditions are good, I don't know anyone (cept' a few americans on this board) who would dive trimix at these depths.
It takes time and experience (short term and long term) to get up to these depths (50 - 55m) on air. In my humble opinion, your friend won't be pushing any dangerous limits, only the limits imposed by an agency that is geared toward a larger diving public that really has no business diving here. With a bit of education, everyone can dive here, on air, with an acceptable level of risk (CMAS and BSAC divers, anyone?). It's wise to learn about narcosis in somewhat controlled conditions, with a diver who has experienced severe narcosis, using narcosis checks throughout the dive, and by remaining very close to the dive partner. I wouldn't want someone to be making their first dives sub-40 solo... that's just unwise.
I think we also need to clear something up... what do you mean by "bounce dives"? Many would assume that your friend will be hopping in the water, dropping to his chosen depth, and returning to the surface. I am reading it like a typical liveaboard diver might use "bounce"... in that your friend plans to drop to his chosen depth and gradually move shallower, only spending a very short time at maximum depth. Please give us some insight.