If you are the seller, you should say, "The initial price was $550 but I could REDUCE (or mark it) it down to $520".
If you are the buyer, you could say,
"The initial price was $550 but I would like to HAGGLE and get the price down to $520"
"The initial price was $550 but I would like to BARTER and get the price down to $520".
To say, "bargain it down" sounds unnatural.
A person can get a bargain or receive a bargain when the price has already been lowered.
If a person talks to the seller and negotiates a lower price, English speakers would use the expressions, negotiate the price, haggle or barter.
If you are good at getting a seller to lower his price by negotiating, you would be described as "driving a hard bargain" or "clinching a good deal".
Hope this helps