Editing bridging transactions in Awaken is similar to handling internal transfers between your wallets.
Instead of simply applying the bridging label, you need to make sure both the send and receive transactions are linked together in order to carry your cost basis forward.
To do this:
Click the checkbox next to both the send an receive transactions to select both.
Click the bridging button that pops up in the small modal.
Optional: in your settings tab, use the toggle to make bridging non-taxable.
This will carry your cost basis forward, potentially leading to reduced overall gains, and long-term gains rather than short-term.