I am playing a chess game and my opponent is black and he asked me if I would accept a draw since I have a King and a Knight while he has a King and a Bishop. I told him that he can make an offer and he mentioned it's against etiquette when black makes an offer. Can you please lead me to locate the source? The game is on GameKnot.com.
There is no such rule.
It would be against etiquette for one side to offer a draw repeatedly, or to offer one in a position which is a certain loss. FIDE rule 11.5 lists "unreasonable offers of a draw" as one thing that can constitute distracting or annoying an opponent, which is prohibited.
In an official over-the-board game, the proper time to request a draw is after you've made your move but before you hit the clock (FIDE rule 188.8.131.52.) That seems to be impossible in an online game, so I would say that it would be best to make the offer right before you move, so that the offer notification doesn't come during your opponent's thinking time.