After mowing the lawn again I now realize the importance of mowing at least once a week during a grass's growing cycle. Lightly raking the side of the house turned up a lot of thatch that was extremely long and clearly choking out the grass (this side also had a ton of weeds, go figure). I may need to get something to dethatch it so the live grass will grow thicker.
The grass trimmings can be left in the lawn IF, and only if, you're only cutting a small amount off the top.
As long as it's maintained effectively, you also don't need to water Bermuda much at all.
So, I'm going to mow every 3 or 4 days to really take advantage of the spring growing period.