Yes, transactions can be sped up in MetaMask by clicking the “Speed Up” button on MetaMask. “Speeding up” a transaction through MetaMask issues a new transaction on Ethereum that has a higher gas price than the transaction that was originally sent. Since the new transaction has a higher gas price, it is more likely to be included in a block. Only one of the transactions (the original and/or the "sped up") will be accepted.
Speeding up a transaction that is transferring funds to the bridge is safe. However, the user interface will not be aware of the new transaction, meaning it may not see the confirmations in the user interface. Once the new transaction has 35 confirmations on Ethereum, check the MetaMask wallet on the Avalanche® Network to see the wrapped funds.
If you do not see the funds in MetaMask after bridging, check here.
Note: Users can NOT speed up BTC bridge transactions.
For a more in-depth read on how the Avalanche Bridge™ works, please read the following articles.