The transactions that correspond to bridge transfers will appear on explorers for the Avalanche and Ethereum networks. It may take a few minutes for the transactions to appear. To search for your transaction in the explorer, copy and paste your address into Avalanche's C-Chain Explorer or Etherscan. To view the transactions sent by the bridge itself, you can look here for Avalanche and here for Ethereum. If you still don't see your transaction, reach out on Telegram or Discord.
For a more in-depth read on how the Avalanche Bridge works, please read the following articles.