There is no such thing as a dedicated bookmark button on twitter. At least not on my client. Twitter on the web or with their app is unusable for me. The only thing I have to find a tweet again is the star / heart button.
Edit: nevermind, I see it hidden in the site's share menu.
I have for years been using the like button as a bookmark tool, and I probably will keep doing so. Old habits are hard to break.