I was in a study in college that studied bone density and different types of exercise in women. I also had quite high bone density compared to the other female students even though I was not heavy yet then, only average. The tech who did the scan quizzed me about my diet and said it was probably because we didn't drink soda in my house growing up (we drank juice, koolaid and milk). She said the carbonation in sodas was bad for bone calcium absorption, and the milk (or other calcium sources) was significant because you can't build bone if you don't have enough calcium in the diet to start with. During the study we all got calcium pills to make sure we had a baseline over the USDA requirement.
The study had a control group who just did their regular stuff (plus the calcium supplement), a running group, and a weight lifting group. I did 2 semesters and was in the control group one semester and the weight lifting group one semester. They told us in a followup that both the exercise groups improved density but that the weight lifting group gained more density. I think I have read since that in general almost any exercise under the influence of gravity (including walking, running) will improve density given sufficient dietary calcium. Other exercises where you are not bearing weight (cycling, swimming) will not help as much although bone will react a bit to the working of muscle against it. Basically bone responds to strain/impact by building up so more strain/impact = more building.
The study doctors REALLY were against carbonated drinks and begged us please to reduce or eliminate them from our diet. They said the problem was both the chemical reaction and that they tended to be substituted in the diet for milk, which for most of the demographic (mainly European heritage white middle to upper class chicks) in the study would have been a big traditional calcium source. Of course you can get calcium from lots of other foods too and for non lactose-tolerant or vegan populations those will be important.
ETA: Just went to look for recent info because college was a while ago

and according to the Mayo Clinic it's specifically cola drinks apparently, not carbonated drinks in general (like mineral water).
Carbonated water and bone health