Sure, wrapping the whole stem section works, but why keep the bananas together? Since most bananas on a bunch ripen at slightly different rates, your prematurely ripe bananas are going to put off more ethylene gas which will only serve to make ALL the bananas ripen that much faster.
Divide and conquer! Separate the ripe fruit from the slightly-less-ripe, wrap their stems in plastic, then enjoy when you're ready.
This should do a couple of things:
prevent ethylene gas from initiating the ripening process on under-ripe bananas
fully cover the stem to really forestall the off-gassing
make your bananas more convenient to grab and enjoy on the go
And if you're bothered by the stem wrapper, try opening your bananas from the opposite end like a monkey. You'll get fewer stringy bits and have a convenient handle to hold onto while you eat. Also, no awkwardness for that final bite.