I feel your pain because my first was like this and at 6 weeks I tried a bottle. Well biggest waste of time and money.
He took it for a week but wasted more formula than he drank because he was only having small feeds.
After a week he flat refused the bottle any more, he went berserk.
Have you tried a pacifier? I feel like you would have better luck there if it's comfort sucking?
At this age it's very normal while horribly draining it will pass.
I'm pro bf but if the bottle is the way you want to go that's your choice, just be prepared it may not work because after 2 months of unrestricted booby she's not going to be impressed likely!
Hope you get some sleep soon, that's the really hard part 😕