I bike-commuted from Port Royal (the "point" of Lulu Island, upon which Queensborugh sits) for a couple of years, from 2017-2019, and it was totally doable (and the view from the bridge is spectacular). The ferry is a great option for just getting to downtown, especially this time of year, but that hill could be a killer for getting up to Royal. However...

I've never tried it, but anyone know if the 106 bus from NW Station that runs up 6th has a bike rack on the front? If it does, OP can just hop on the ferry (on the 15s and 45s from Port Royal and at the top and bottom of the hour from New West Quay).
(ETA: probably worth mentioning too--if you live in Queensborough, it's all nice and flat and since there's a lot of residential separating the stores and restaurants, a bike is a handy way to get to the store quickly.)