This is largely going to just require slight modification for any other appimage.

Create a file named /home/jdboyd/.local/share/applications/bitwarden.desktop
and give it the contents of:

[Desktop Entry]
Type=Application
Name=Bitwarden
Icon=/home/jdboyd/.local/bin/bitwarden-256.png
Exec=/home/jdboyd/bin/Bitwarden-2024.10.2-x86_64.AppImage
Terminal=false
Hidden=false
Categories=Utility

Also download the png icon from https://github.com/bitwarden/brand/blob/main/icons/256×256.png

Then place it at /home/jdboyd/.local/bin/bitwarden-256.png

Now the application can be launch from the dock correctly.