The Avalanche Bridge™ uses Chainlink price feeds to get gas price information for the Ethereum network. The gas price used is higher than the Chainlink FASTGAS value and the Geth gas price approximation. The gas price is padded by a few GWEI to ensure transactions sent by the bridge are quickly included in an Ethereum block.
The Avalanche Bridge also uses Chainlink price feeds to determine token prices used to calculate the amount of a token that is equivalent to the bridge fee.
For a more in-depth read on how the Avalanche Bridge works, please read the following articles.