Hi Bree,
I quite understand your sentiments, bicycles are (usually) a lot less shocking, but for that very reason also less easy to remember. Rape is an astoundingly common theme in films (I found out when thinking about it), I could cough up 30 or so titles without too much thinking, so we would have reached 50 in a jiffy

. Velocipedes it is, though, so here goes:
8. Il Postino (1994), postman on a bicycle
9. Jour de fête (1949), Jaques Tati as postman on bicycle
10. Dream, De (1985), Ymkje cycles to town to denounce her lover
11. Het Meisje met het Rode Haar (The Girl with Red Hair, 1981), resistance fighter transports illegal publications on bicycle.
12. Offret (The Sacrfice, 1986), another postman on bicycle
13. Rukajärven tie (Ambush, 1999), bicycle scouts during the war
14. La Vita e Bella (Life is Beautiful, 1997), Roberto Benigni on bicycle
15. Batoru Rowaiaru (Battle Royale, 2000), schoolboy rides a bike before getting killed.
16. Io non ho paura (I am not Afraid, 2003), village kids cycle through the countryside
17. The Muppet Movie (1979), Kermit rides a bike
18. Kundskabens træ (Tree of Knowledge, 1981), bicycle lamp is used to light up winter scene
19. A Bridge too far (1977), resistance member spies on Germans using bicycle
20. Le Temps du Loup (2003), destitute family moves around with one bicycle