Andrew Scott was locked up for 16 months after a court heard how he targeted the youngster when she was aged nine and ten.
The victim was not a child he had responsibility for as a foster parent.
Leeds Crown Court heard Scott sexually assaulted the girl on three occasions over a period of 12 months.
The offences included him touching the girl's chest on one occasion.
The other two offences were carried out while they were travelling on a bus.
Police were contacted when the victim broke down in front of her mother and told her about the offending.
Scott, of Leicester Close, Woodhouse, was interviewed and initially denied the offences.
He later pleaded guilty to three offences of sexual assault of a girl aged under 13.
The 55-year-old appeared in court without legal representation as he said he could not afford a barrister and could not obtain legal aid.
"I am sorry for what happened and I apologise for it all."
The court heard Scott is a former foster carer who has a wife and family and has served in the Royal Air Force.
He has no previous convictions.
A probation service report assessed him as posing a high risk of harm.
Sentencing Scott, Judge Robin Maris said there was an element of grooming and planning to the offending.
He said: "You made denials and I have read with care how this has had a psychological effect on her.
"These offences are so serious that only an immediate custodial sentence can be justified.".