Voy a mi bicicleta means you're going to your bike. In Mexico we say "ando en bicicleta". This simply means you usually use your bike as transportation, or that you're going for a ride (Voy a andar en bicicleta). "Paseo en bicicleta" means you're using it to enjoy the view and have fun.

Voy a pasear o montar my bicicleta.

Nosotros decimos: *Voy a montar mi bicicleta,or *voy a pasear en mi bicicleta.

"Montar en bicicleta" Montar = to ride ( bicycle, horse...)

You mean: Ando en bicicleta; Paseo en bicicleta. Futuro: voy a pasear en bicicleta