Not disbelief, just reasonable skepticism.
Anyway, cycling at a moderate intensity would be a good way to get in an hour or so of cardio on most days of the week, and could be done in conjunction with your lifting. If you eat enough, and hydrate properly, this shouldn't keep you from gaining in the gym.
It would be best for your leg days to coincide with cycling off days, when possible. Not sure of your lifting schedule and your splits, but you get the idea here. When you're riding on the same day as another workout (upper or lower body), lift early in the day, and ride as a recovery type of activity later on...maybe a before/after work, or lunch/evening kind of separation. The order isn't as important with upper body work, but put your priority worjout first,and then it's warm down, eat your 3 to 4:1 CHO
rotein, hydrate, and rest.
Since you like riding, but it isn't your priority and you don't need to do intervals or other very difficult work, it doesn't matter if you do it fatigued. I'd keep up with my nutrition and hydration, but otherwise go out and enjoy yourself. If anything, it should actually help your recovery.
For you, though, it sounds like you just need to eat more (as well as keep lifting). If you gained a bunch of weight during basic, where you get your fair share of jogging and marching (if I'm not misinformed), eating 5 times a day was certainly a part of it.