A 65-year-old man has been refused bail after he allegedly assaulted a 12-year-old girl and made sexual remarks to her while she was catching a bus to school in Sydney's east on Thursday.

Police say Glenn Maguire, of Eastlakes, boarded a bus in Darlinghurst about 8am on Thursday and sat next to the girl, who was already on board.

As the bus was travelled towards Waverley, he allegedly started asking the girl personal questions, made sexually suggestive remarks to her and grabbed her arm as she was trying to move away.

He got off the bus at the same stop as the 12-year-old, on Bronte Street in Waverley.

The girl ran to her school and reported the incident to her principal, who rang police.

Police arrested Mr Maguire outside a building on Bronte Road about 8.30am on Friday.

They charged him with intimidation, assault and inciting a person under 16 to commit acts of indecency.

He was refused bail at Waverley Local Court on Friday and will re-appear at court on April 8.