Leaving aside the issue of whether transporting your bikes is worth the hassle, keep in mind that for almost any type of cycling that one would enjoy, that type of cycling is available in Alaska, although probably in smaller doses than one's home location. I would offer that there's probably decent opportunities for a moderately competent cyclist (of whatever discipline) and not as many opportunities as one might want for the very casual rider.
Road biking? Got it. Won't be quite as nice as some road cycling in the L48 and there won't be too many dedicated/protected road races in AK, but there is road biking.
Mountain biking? Got it. Lots of places to go...but perhaps more favoring gravel roads than single tracks like one might find in the mountain West. There are places where one can just head "that direction" for as far as one cares to go, land ownership issues and the like mean that, for it's size, AK doesn't have much in the way of off-road trails. Some state parks have biking trails, others don't, and even where there are trails, they can be closed frequently for a variety of reasons
Piddle around town? Got it. Certainly in Los Anchorage and Fairbanks, including with bike trails. Moreso, and more enjoyable IMO in Palmer, Talkeetna, etc. This sort of biking is probably most worthwhile if one is at a small location for several days rather than just passing through.
Piddle around campgrounds? Got it, but see the note about mountain biking. Many of the "Campgrounds" will be dirt or gravel parking areas that are readily cycled with one's mountain bike. Some of the 3-wheel grocery getter bikes that are often seen at RV Campgrounds in the L48 wouldn't be very beneficial in AK.