Cable cars
There are several cable cars to transport cyclists in and around Bolzano. Colle/Kohler, San Genesio/Jenesien and Renon/Ritten for example. Furthermore, in Appiano/Eppan the Mendorla cable cars bring you up to Mendorla. The most well-known is probably the Colle cable car. The downhill track back to Bolzano is nothing for the faint-hearted.

No-goes
The journey with the Renon cable car up to Renon/Ritten is fast and much easier for cyclists than cycling up the 1000 metres of difference in altitude. However, it is an absolute no-go to cycle directly back down to Bolzano. Why? The hiking trail is for hikers and is not a sign-posted downhill track! Cycling is expressively prohibited on this path.
Also in Monticolo Forest there are some trails which are highly frequented by hikers and are therefore not open for mountain-biking.