To communicate with a Garmin inReach device, the inReach must send the first message to your Bivy Stick. Garmin inReach devices do not allow phone numbers to initiate the first conversation, so they cannot receive an incoming message until they have first sent one.
Once the inReach user sends a message to your Bivy Stick, you'll be able to reply and continue messaging back and forth without any restrictions on the Bivy side.
You can find your Bivy Stick's phone number in the Bivy app. While connected to your device, open the main Bivy Stick page, and your assigned phone number will be displayed there.