Onion sets are second year onions so it is natural for them to bolt and a reason why the majority of my onions are grown from seed (they very rarely bolt in the first year-maybe 2% will try this).

I cut the flowers off and that seems to help to get the bulbs bigger.

Hello , I grow both onion plants and sets. Just clip off the flower stalk. If you don't your onions will have a hard core in the center and will not keep very long.
If you want really large sweet onions next year, may I suggest you get a catalog from Dixondale Plant company. They have onion plants for different regions of the country that will grow well for your area. The onions are resonably priced especially if you get some other people to share an order. This year I planted 9300 onions from Dixondale and 20 pounds of sets for my Market Garden. All are doing very well with our cool Spring and ample rain . Check out Dixondale's on line catalog.
Linda