Fitbits struggle to track any activity that isn't mainly steps such as cycling, rowing and weights. The problem is that they track steps and you just don't take steps when spinning.
Some people find that they can get a reasonable "step" count by putting their fitbit on their ankle (I'm not sure if this applies to you as I don't know what model you have). The problem with this is that fitbit doesn't know what you are doing and will get the calories calculation wrong.
The way to get the more accurate data is to tell fitbit what you are doing and we do this by manually logging the activity using this procedure:
http://help.fitbit.com/articles/en_US/Help_article/How-do-I-log-or-record-an-activity/
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