Bogota is fantastic for cycling, you should definitely bring your bike if you can (a small bike box/bag counts as a normal bag on Avianca with no extra charge), though I'd recommend bringing the winter bike due to mainly the weather (it usually only rains in the afternoon, but any given day in Bogota it can rain at any time for any amount of time) and also the small risk that you can, unfortunately, get bike jacked. I mean, you see guys riding Di2 Tarmacs and Dogmas solo around Bogota every so often but I wouldn't risk it myself. Colombians are generally nice but be wary of anyone being too friendly.
Early in the morning is the best time to go out for a ride. Patios (
https://www.strava.com/segments/5222513) is the local climb, Saturdays and Sundays it's jam packed and pretty safe (just try to keep right) past midday on the weekends (I'd suggest early and not-even-bright on weekdays). Try extending it to the Vuelta a la Sabana (
https://www.strava.com/segments/2499488), clockwise or counterclockwise, or even adding on the Cuchilla de Guasca (
https://www.strava.com/segments/1303263) if you want a longer outing within the general vicinity of the city. There is also a pretty decent cycle path network (
http://www.mejorenbici.com/comunidad/ciclorutas) if riding in the roads seems dangerous at first. You can also ride in the bus lanes (not the Transmilenio ones, though), but not all bus drivers seem to know this, so be careful. City streets are absolutely awash in potholes, but the roads in and out of the city are pretty well kept (they're toll roads - but are free for cyclists).