Without a proper assessment from a medical professional, it's impossible to say if you are unhealthily underweight: any measure such as BMI is a necessarily broad scale. If you are in any way concerned, go see your Doctor.
If you do want to "bulk-up" usefully, the following should be remembered: exercise - nutrition - rest. Exercise provides the stimulus your body needs to change; nutrition fuels the change and rest provides the opportunity for that change to happen.
Compound, weight-bearing exercises focusing on the big muscle groups will produce hormones that will stimulate the whole body to grow, not just the targeted muscles. Deadlifts, squats and the chest press are good examples. Additionally, weight-bearing exercise addresses the decline in bone density (which accelerates past forty years old) which cycling doesn't.
Eat more, smaller meals rather than fewer, bigger ones, about five or six times a day. Three hours after a meal have a snack, two and a half hours after a snack have a meal; this will keep your metabolism fired-up, rather than peaking and slumping as with the traditional "three square meals a day". Breakfast should be larger than Lunch which should be larger than Dinner.
Getting sufficient rest means sleeping enough and not over-training. Eight hours sleep is a good starting point: if you need an alarm clock to wake-up, you're not getting enough. Allow at least a day and preferably two between gym sessions: once or twice a week is plenty to get good results. Gym-fascists who do whole-body workouts five times a week are idiots; "no pain, no gain": b*llsh*t.
But before you do anything else, get professional advice: until you know where you're at, you can't decide where to go!