Ryan, 39, had drunk a bottle of port in the airport lounge before boarding a British Airways flight from Glasgow to London City Airport on 31 July, Ealing Magistrates' Court heard.
One flight crew member said the pop star had told her he wanted an upgrade and asked her if she knew who he was.
Ryan, who denied all charges, said his behaviour had been "playful".
The boyband star, who said he lived in Spain, was found guilty of being drunk on an aircraft, assaulting a police officer by biting him, racially aggravated common assault by beating and behaving in an abusive way towards the cabin crew member.
He is due to be sentenced on 24 February.
After the hearing, members of the press saw Ryan, who was given unconditional bail, running into a nearby primary school to avoid photographers.
Blue released three studio albums in the early 2000s, with hits including All Rise and Sorry Seems To Be The Hardest Word.
The band split in 2005, reforming six years later for the Eurovision Song Contest.