Now Omnivore is dead, it would be great if Bullet could fill that gap

If I understand it correct, yes, that is much needed:

Basically, I'm in the middle of something else (eg reading), come across sth to follow up later on, but may not remember the exact loc / address / title etc, so i'd like to copy the link or a screenshot and add as an item to my list of things to f/u. Rn every other app shows up on that list to plant my copied link into, except Bullet...

Same with photos etc. You could share anything basically and have it share to Bullet. Similar to the way Google Keep works. Share a photo, link, note, whatever you want essentially. :)

One user is interested in using a share feature to create shortcuts that let you record voice entries into bullet inbox on the fly