With verbs of motion like ездить you use на + prepositional case for means of transportation and в or на + accusative for destination, but with билет you use accusative for both. Is there a reason for this?
билет 'ticket' needs the prepositions
в + a noun in the Accusative case, the choice of a preposition depends on what the ticket is used for.
• With kinds of transport
на + Accusative is used:
билет на самолёт – airplane ticket
билет на поезд – train ticket
• With entertainment, sport, etc. events
на + Accusative is used, too:
билет на концерт – concert ticket
билет на футбольный матч – ticket for a football match
в + Accusative is used with the names of buildings where entertainment events take place, like theater or cinema:
билет в театр – theater ticket
The use of the Accusative case is due to the fact that those expressions really denote the destination where you will go with that ticket.
And naturally, as @user31264 wrote in his comment, with planes you use
летать на самолёте, not
ездить на самолёте, because
ездить means 'to travel on land transport', or 'to travel on a kind of transport', but in this latter case you dont specify the kind of transport. If a European says "Я часто езжу в Нью-Йорк" – "I often go to New York," that would surely imply using either ship or plane.