What's the term for elastic pricing?
Perhaps you may want to look into Price Discrimination? This however is the concept of companies varying their prices on different consumer markets. 

1st degree price discrimination, at it's most optimal, is when companies charges the price of each individual consumer's demand. Those willing to pay the most will pay the most. Your description resembles this procedure, but it is not quite exact. Yours implied bargaining, which may or may not lead to 1st degree price discrimination. 

2nd degree price discrimination is setting variable prices depending on the product or the quantity sold, playing off of the consumer's preferences. 

3rd degree price discrimination is the segmenting of a market into smaller markets (based on some characteristic), and charging a uniform price in that market. The price between these segmented markets vary.