Knowing that Sirius likes boys and girls hurt Remus a lot more than he would care to admit. If Sirius just liked girls then Remus would be able to accept that he didn't stand a chance and be able to to try and move on. As it was, Remus knew that Sirius liked boys as well, and he just wasn't one of them. Instead he just kept his feelings locked away, and tried to be happy for Sirius whenever he flirted with someone new, or worse when Sirius actually got together with someone.
It seemed that Sirius liked everyone apart from Remus.

Believing that Remus only liked girls hurt Sirius more than he could say. He had grown up being told that no one would ever love him, so anyone who showed some kind of love would make him feel as though he was proving his family wrong. Sirius spent half his time wishing that Remus likes him, but accepting that it would never happen. He would date anyone who showed interest all with the intention of getting over his best friend. He never loved any of them, not in the same way as he loved Remus.

Lily heard Remus' side of the story during prefect duties.
James heard Sirius' side of the story during Quidditch practice.
Both were made to promise not to tell anyone, and as good friends would, they both kept their friends secrets.

Everyone could see that Remus liked Sirius and Sirius liked Remus, but both were too stubborn to admit their feelings for the other.

Sirius and Remus never got together in the end, both too scared to tell the other. Remus feared rejection from both the muggle and the wizard community. Sirius was scared of ruining his friendship with Remus.