“For example, suppose a market participant was selling the EUR forward against the USD. Given the USD/EUR quoting convention, the EUR is the base currency. This means the market participant must use the bid rates (i.e., the market participant will “hit the bid”) given the USD/EUR quoting convention.”
If you have a bid-ask spread on oil of $31.50–$32.00 per bbl, the bid is the price (in USD) that they’ll pay to buy a barrel of oil, and the ask is the price (in USD) that they’ll accept to sell a barrel of oil.
As it is with oil, so it is with currencies.
Given a USD/EUR quote, the bid is the price (in USD) that the dealer will _ pay _ to _ buy _ one EUR, and the ask is the price (in USD) that the dealer will _ accept _ to _ sell _ one EUR.