I overseeded last fall and am now seeing the bermuda come back in. It will be a little bit splotchy for a while but I find that it is not that hard to stress the Rye to the point where it dies off quickly - frequent, close mowing (scalping) for a few weeks this time of year kills it off for me, as it warms up the bermuda (low growing) outcompetes the Rye (Vertical growth habit) and the rye dies off pretty fast. I also lay down a healthy dose of milorganite and one of the good organic blends (I like calloway's, - it seems low on odor). I mix in blood meal for a little extra protein and iron to get that nice dark green look. I'll also spread a little screened compost over any low spots since I prefer a very unifom lawn.
Oh... and I will hit it with some sprayed molasses as that seems to melt the thatch and speed things up.
At the moment, my yard is so full of little worm piles that it looks like it just got aerated....
One-two good weeks in the 80's with plenty of sunshine and the rye will be gone except in the shady spots where it lasts a bit longer. Rye seems to love water so I let it dry out pretty good between waterings if possible. Combine that with the stress of hacking off 2/3 of it's growth a few times, the Bermuda fighting for nutrients and the rye gives up the ghost