When Geoffrey's identity was revealed to Emily, he expected that she will be reluctant to forgive him. He knew that she was a bit prideful like that. Since he was at fault, he took the initiative to lower his ego and apologize wholeheartedly.
When they were paired up in music class, it gave him the opportunity to continue with his apologies. He wanted her forgiveness not only because he thought he loved her, but because he considered her as a special friend close to his heart.
Like any other matter in his life, he tried to repress his emotions for although he fancied himself in love with her, he was still bound to an obligation. So, during their rehearsals together, he never initiated to voice his real feelings. He kept his silence and tried to treat her with utmost care and respect.