Blockchain can do without Bitcoin, but Bitcoin can't do without Blockchain. Blockchain has been around for long, but there was no use for it for as much as I can remember. So, Bitcoin played the key role of making Blockchain popular. It was after Bitcoin was created that people started to think of other ways that the Blockchain can be used. As for now the only thing that has been achieved with Blockchain is just the transaction part and nothing else. Other things that has been said to be possible includes voting, education, etc. Let's look forward to all that.
So, you can understand now that blockchain technology is something which makes bitcoin possible. It is kind of distributed ledger where our bitcoins resides and our transactions are recorded in a manner no one could manipulate on own wish.
I always wonder on in what other possible ways bitcoin would have been designed along with no central authority to issue bitcoins and to verify bitcoin transactions? I could not find an answer for it. So, to have a decentralization, we must need blockchain to govern all these things yeah blockchain is taking care of what a central authority or a engine (the core part of a software) in a software/business is doing for example paypal (issuing of new money is missing).
So right now, the rise of blockchain technology is owed to bitcoin. It makes this technology popular to many. It paves the way on realizing that blockchain tech has a lot of benefits if utilized correctly. So right now, we are grateful that bitcoin is invented via blockchain tech. It opens a lot of doors for this technology.