You dont need to proof dought before you roll you bagels just let rest 10-15 minutes.Also do you add some high gluten flour to your dough?
Malt syrup is also good in bagel dough.Heres my recipe from a bakery I worked at many years ago
This makes about 120 bagels
1 gallon water
2 cups malt syrup
5 oz salt
1 oz cold water yeast
1/2 flour +1/2 hi-gluten flour
I dont have the amounts of flours because all our doughs,bagel,croissant,danish, breads and so on. we made by feel of the dough as the flour has a tendency to dry out at high altitude
Mix and add flours untill somewhat firm but not sticky
Let rest on bench a few minutes
Then roll out bagels.
Lay on corn meal proof;boil and bake
I used to be so good I could make the dough and roll out 119 -120 bagels in less than an 1/2 hour every day.
Alas that was a long time ago.