When you are bridging over a new token, that action will require an approval transaction fee.
This goes to Ethereum block producers, not to Arbitrum.
The approval transaction only applies once per token, per wallet address.
This means that the next time you want to bridge this token over, you will not have to pay for an approval transaction.
However, if you want to bridge the same token over from a new wallet address, you'll have to pay for the approval transaction again.
Your wallet will prompt you to complete this transaction.
After your transaction has been approved, you will be prompted to pay the standard deposit fee.
You will pay a deposit transaction every time you want to bridge over funds. The deposit transaction goes partly to Ethereum and partly to the Arbitrum node validators.