You can start with the Append journaling action in the Bear integration guide and make some modifications. It does similar to what you describe.
The title parameter in the URL determines how the note in Bear will be named. The text parameter controls the actual text to be appended. Bear will take care of creating the note if it does not exist.
Something like the below sounds similar to what you are describing:
bear://x-callback-url/add-text?title=[[date|%Y-%m-%d]]&text={{[[date%H-%M] ]}}[[draft]]&mode=append
Here the title will be the current date formatted like 2018-07-05 and the text appended will be the content of the current draft with hours/minutes before it.