A market maker who is quoting a price of 1.2000 / 1.2005 for EUR/USD is indicating a willingness to buy EUR/USD at 1.2000 (the bid price) from you and sell it at 1.2005 (the ask price) to you.
When thinking about bid and ask price, think about it from the perspective of the person on the other side of your trade.
Bid is the person coming up to you, "I'll buy X from you for Y price." (You sell to him)
Ask is the other person coming up to you, "I'll sell X to you for Y price." (You buy from him.)