Bici vs. bicicletta

'Bici' and 'bicicletta' are both Italian words for bicycle, but they differ in usage and formality.

Bici

'Bici' is the informal, shortened version of 'bicicletta'. It is commonly used in everyday speech.
Vado a scuola in bici.
(I go to school by bike.)
La mia bici è rossa.
(My bike is red.)
Andiamo a fare un giro in bici?
(Shall we go for a bike ride?)

Bicicletta

'Bicicletta' is the full, more formal word for bicycle. It is used in official contexts or when emphasizing the complete term.
Il negozio vende biciclette di alta qualità.
(The shop sells high-quality bicycles.)
La bicicletta è un mezzo di trasporto ecologico.
(The bicycle is an eco-friendly means of transportation.)
Ho comprato una nuova bicicletta da corsa.
(I bought a new racing bicycle.)

Summary

While 'bici' and 'bicicletta' both mean bicycle, 'bici' is more casual and commonly used in everyday situations, whereas 'bicicletta' is the full, more formal term used in official or specific contexts.