Most activity trackers like FitBit and apps like MapMyRun and Runkeeper track based on detectable forward or upward motion, so if you're on a stationary bike, it won't know that your active (and MMR and RK, etc. require a smart phone to passively collect your data). That said, all of these apps and devices include the ability to log on to a web-based dashboard and manually enter your activity and some gyms have equipment where you can plug in a USB thumb drive and have it download your workout stats so that you can upload them to a fitness program.
Make sure that your employer's program will accept manually-entered workouts for the fitness bonus. If they will, then whatever program you like and they accept should be fine, you'll just have to update your info on-line each time you work out.
Heartrate trackers such at Garmin will probably do what you need because it tracks your heart rate, not just whether or not you're in motion in a way that can be detected. Those can be a bit expensive though, but friends who have them really like them.