100 miles a week isn't so much volume that it should hurt you in the gym, but I'd be eating before, during, and after to make up any calories. bodybuilders typically gain mass, then shed fat, btw, rather than doing it all at once. The idea is to gain muscle, if it means putting on a little fat to make sure they maximize the lean mass gain. Before a competition, they "cut."

If you don't really care about getting faster, you can keep your rides at a moderate intensity (12-15 RPE) and still get cardio benefits; there are benefits above this, but doing intense cardio isn't really conducive to gaining weight (duh). This will conserve some calories and save some training stress.

For general health, it's great to incorporate strength training, but the cardio factor is much more important. I used to be basically an all-weights kind of guy, with the attitude that "exercise is exercise, right?". You'll find a lot guys like this at your local gym. Then I went to school for exercise physiology, which reformed my views quite a bit. In a nutshell: no, adaptations to weights and cardio are not even close to the same, in any way. There's a lot more to it than body weight and calories, just as there's a lot more to nutrition than fat, calories, and vitamins. Sorry, that's my PSA for the day.

No criticism intended, just meaning to stimulate some thought as to why you want to gain a bunch of weight. I've been there before, and it took some thinking for me to realize that it wasn't actually what I wanted. Not to mention that my food bill was insane, and I wasn't even eating very good food. I'm a lot bigger than you (6'1", 158 lb), and it takes a lot for me to gain weight.

I realized that I thought I was small, because of all the athletes I saw in the gym who were much bigger than I was. You know, the 200+, lean six-footers. But they just had different body types, and are actually atypical. Some guys here wish they were closer to your size. That's a climber's build, though slighter than most.

Basically, I'd advise anyone to find some activity they really like to do, and do that. It's much more likely you'll develop a healthy lifestyle around something you like, than something you think you should do. Luckily, that's cycling for me. If it's bodybuilding for you, that's great. If that's more your thing, you're likely to get more (if not necessarily better) advice on a bodybuilding forum. You're more likely for someone here to tell you that lifting weights is totally useless, though they'd be wrong, of course.

A side note: you added 25 pounds to a 5'4", 100 pound frame? Are you sure? Was it actually mostly lean (was your body fat measured)? You'll hear of 200+ lb baseball players showing up to spring training with "20 lbs of muscle" added from last year. Usually, though, they mostly just look pudgy. They may have gained 20 lbs, but it certainly wasn't all muscle. It's hard to gain that much lean mass, period, let alone in a period of a few months. If you were still growing and developing (were you in high school?), that's a different story, but that you're back down to 100 leads me to believe that isn't the case.