Paypal adoption is driving the price up. Hard to say where it will end. The plan is to allow people to not only buy bitcoin but also use crypto to pay for goods as part of the Paypal ecosystem.
In regards to the concept that Bitcoin will become 'money'. I think that is the wrong way to look at it. Bitcoin will become a store of wealth. No one will ever want to use it again to buy a pizza. As already discussed its value is in its absolute hard-coded supply and the inability to print more.
This makes it inherently rare... far more scarce than gold which is being dug out of the ground all the time. Whilst once bitcoin keys are lost, that bitcoin is gone forever.
This also makes it unfair, unfair that white techno nerds hold the vast majority of it and continue to accumulate it. Unfair in that it will never bring financial liberty to the worlds poor as some libertarian bitcoin evangelists try and preach. Unfair in that it is increasingly being bought up by investment portfolios and big business, who will lock it up in their vaults and the common man will never get to own Bitcoin.
Buffets argument that it has no inherent value, (you can't make silicon chips out of Bitcoin like you can gold) is a very old fashioned way of looking at the world. You shouldn't be able to bundle up sub-prime mortgage debt and sell it on an open market as an asset, but banks did. Concepts and computer code are as real as any precious metal today, and Bitcoin is the distillation of that.
*disclaimer; I own some bitcoin. I believe it will become a well respected store of wealth. I also never invested more than I am happy to lose. Bitcoin could drop to $0 tomorrow and anyone buying it should be prepared for that. It is a massive, very expensive experiment. It also paid for my cats extensive medical bills and my beemer. So for me on a personal, very selfish level, bitcoin has already succeeded.