They mean about the same, but bargaining implies a buyer and seller discussing price only, while negotiating suggests a broader discussion that involves items other than price. I will bargain with the rug dealer to determine the lowest price for which he will sell it to me. I will negotiate while buying a home, offering a higher price in exchange for items I desire (furniture, new paint, etc) or conveniences I desire (a preferred move-in date, inspections, etc).

negotiation - переговоры, to bargain - торговатъся (забыл как пишетъся)