v.1. To increase the price of something by offering increasingly high purchase prices for it: The traders bid up the stocks in oil companies. The buyer bid the artist's paintings up much more than she expected that they would be worth.
2. To increase some cost by offering increasingly high purchase prices: There were many potential buyers, and together they bid up the cost of milk to $3 per gallon. The price was low at first, but the buyer bid it up to much more than he could afford.