Factually talking about systems, we gotta make two bold headlines about each one: Bootstrap has been around for a while, has a vast community and much probably will not be gone in a while. Tailwind in the other hand, is the trendy framework starting from the past year. Referring to UI, I really prefer Tailwind, however I can't ignore the fact that a lot of libraries that emerged felt short in the end after a few years (a point where Bootstrap kept his status).
You are able to use both them together but I advise you — it will be a mess. And you gotta hope that you won't have any kind of conflicts between class naming and other general styling.
My recommendation would be to use one and only one. Perhaps rebuild the UI with a specific framework in mind, otherwise you will start to workaround things of both frameworks to contradict each other - and your team (if you work with one) will hate you.