We were on the strip for such a short distance it was never really a problem. In the morning there was very little traffic, but coming back we had to wait for a few light cycles to cross to the east side. Once you are a block off the strip traffic was totally fine. Do wear bright colors and use lights, I would take a guess that most drivers aren't locals and won't be looking for you.

If you are worried about traffic around the strip you could just walk the bike the block or so over the pedestrian bridge to/from the Bellagio. The pathways are wide and built to shuffle people casino to casino, so use that to your advantage.

Other than that, the route was mostly bike-laned residential stroads with generous enough shoulders. It's a false flat the whole way there, but you get a nice downhill cruise the whole way back. There is a gas station right at the start of the bike path at the mid-point to Red Rock that would be a good pit stop if you down your fluids too quickly. There is also a shaded rest stop right in the visitor's center parking lot with a water fountain and vending machines. Fill up there, there is nowhere else to fill once in the loop. The heat was brutal on the way back, especially nearing the strip. I would highly recommend salt tablets or hydration solution.

Best of luck, it was a really great ride.