Years? Absolutely not. Transfer can be done in about 90 days, less (30 days) if you pursue aggressive entry, high orbit refueling, and nuclear thermal propulsion. Assuming you're settling the place and not just doing flags and footprints, transfer time is the important part.

That's astoundingly quick. 30-90 days is in the same range as crossing the Atlantic via tall ship. With transfer time that low, it really does seem feasible. The two year gaps are a bit rough, but there are plenty of ways to plan for it.

Nowadays ships cross the Atlantic in less than a week.

Well, if any of these silly EmDrives ever work out, maybe we can get Mars down to that time too.

For the journey, yes. But for permanent settlement, in both cases you'll need of the order of years-worth of supplies while you become self-sufficient.

Back on-topic, the discovery of water on the moon makes this more achievable there; otherwise Mars's resources might have actually meant less resources were required.

You don't have to send all the supplies at once though (you shouldn't actually). You can send many small missions, each providing some parts of a Mars base before sending any humans. See for example the Mars Direct plan by Zubrin: https://en.wikipedia.org/wiki/Mars_Direct

But the presence of water on the Moon is more limited than the presence of CO2 and H2O on Mars. That could be significant for self-sufficiency. Especially if we could find a way to make plastics from CO2 and H2O in a reasonably small mobile device. Just grow your colony out of the stuff you suck out for the atmosphere...

You don't need radiation shielding to go to or stay on Mars. The health risk from the excess radiation is moderate, should be a very low priority for an adventurer.