The bridge charges transfer fees in order to cover the cost of the transaction fees on the Avalanche and Ethereum networks. These fees are charged in-kind with the ERC20 asset being transferred. That is, when you transfer a token, a portion of the balance transferred is taken by the AB as a fee.
When moving assets from Ethereum to Avalanche:
If you're transferring less than $20 of assets, the fee is 5% of the value of the assets transferred.
If you're transferring more then $20 of assets, the fee is $1.
For a limited time, this percentage is zero to encourage users to transfer assets. Further, transfers to Avalanche may qualify for an AVAX airdrop as described here.