If you still are going low despite eating beforehand you should probably ingest carbs during exercise, too. Try using a sports drink instead of water while you're on the cycle and treadmill. Sip liberally throughout your workout. Smarties and glucose tabs are also good ideas.
You can also eat more carbs before exercising. Try Clif bars- 45 g - available at most sporting goods stores and at Costco. Half a peanut butter sandwich with a half glass of milk is also good. For me. As Tom T suggest, don't bolus for these carbs if you'll be exercising within an hour or so. At least reduce your bolus - I reduce mine by 1 unit per 30 minutes of planned exercise.
Aerobic and endurance exercises tend to drop BG because your body is using up glucose. Anaerobic exercises like weight lifting or sprinting tend to raise BG because your liver dumps glycogen into the blood, perceiving an emergency need for more energy right away. (That's a very simplistic explanation.) But weight lifting will often only raise BG if you're doing heavy weights and low reps - light weights and low reps less so because it's more like aerobic exercise. I would recommend adding the weight lifting BETWEEN cycling and the treadmill.
Keep trying different things until you find what works best for you. There's no single answer that will work for everyone.
There's great information about exercise and blood sugar in the Diabetic Athletes Group here, where this subject comes up all the time or in the books Think Like a Pancreas or The Diabetic Athlete.