Rising of Bagels Made Using Starter
I have made bagels before but this is my first time making bagels using sourdough starter rather than commercial yeast. My dough was incredibly dense, did not rise, and did not follow the float test as I would have suspected.
I used rossnroller's recipe posted here: http://www.thefreshloaf.com/node/17328/sourdough-bagels-my-weekly-treat 
I followed the ingredient list and instructions, but I swapped out some of the white flour with 130 grams of rye flour. I used Bob's Red Mill Whole Grain Dark Rye Flour. I used a mixer to make the dough. The dough was very stiff and dense. I tried the windowpane test but got nothing. Perhaps, I could have hand kneaded instead of using the mixer.
I let the dough ferment for 5 hours at room temperature after mixing, expecting it to double but it didn't at all. Then, I placed it in the refrigerator overnight. It didn't change at all when I took it out of the fridge in the morning. I placed one of the yet-to-be-cooked bagels in a bowl of water to see if it would float but it did not. The same is true when I placed it in boiling water.
Here's a photo of the dough prior to baking:
I don't know why my dough did not rise. My sourdough starter was in good shape. I fed it 5 hours before mixing and it had doubled as expected. So, I suspect that the rye flour is the culprit. I know that rye flour is prone to having a dense, cake like structure, so that may have interfered with the dough's ability to form gluten. If its not the rye flour, it could be the lack of proper kneading for gluten development.
Luckily, the flavor of the bagel was excellent, but the texture could have been better.
Bagels After Baking:
1) Is it necessary for the bagel dough to float in water especially considering that I used starter rather than commmercial yeast?
2) What was the problem with this batch and what could I do next time to improve the rise of the dough?
3) What is the max amount of rye flour that could be in the dough?