I saw an ad for this in the tram and decided to look into it a bit more.
On 14 and 15 December, Velafrica will be holding a special collection drive in Bern. The organization refurbishes unwanted bicycles and and ships them to locations throughout Africa. Short video here: http://velafrica.ch/de/Was_wir_tun
The website also says there are drop-off spots throughout Switzerland. You can search here for a location near you: http://velafrica.ch/de/Machen-Sie-mit/Sammelstellen
I have no affiliation with the organization. I thought it was a nice idea to take unwanted bicycles and send them to folks that could use them instead of taking them to the tip.
Website says English is an option but most of the pages don't function properly. Stick with DE or FR, or try your luck with Google Translate.