When I tried to enter that into a new bitcoin wallet app called Bither, it asked me for a password. I entered my passphrase from Bitcoin core, yet it doesnt work.
Using the same password in different applications is a security risk. Bither asks for your Bither password, not your Bitcoin Core password.
Now my question is, in order to transfer the bitcoins, do I need to have them be delivered to my wallet in bitcoin core first?
No.
Also what can I do about the space issue? I tried pruning, which from what I understand is when you open bitcoin.conf and write "prune" in there. Of course, it didnt work.
Enter this:
prune=550
This reduces the blockchain to the last 550 blocks. Including chainstate, it will take less than 10 GB (but still requires downloading the full 190 GB blockchain).
I use and recommend Electrum, easy enough to use and learn, and good enough for more advanced use. Should be really easy, since you seem to have your private key already. Just install, and on the very first window to create a new wallet, select the last option "import Bitcoin addresses or private keys".
Agreed. I would choose Electrum over Bither too.
Also, seems yr private key is compressed... Get the uncompressed key via
https://www.bitaddress.org (run offline) and import that.
The uncompressed key would lead to another address. Importing the compressed key into Electrum should just work. Unless you're using a SegWit address, in that case you're going to want to read
this guide.
Now I can start uninstalling that huge bitcoin core nonsense!
Don't dispose of Bitcoin Core for the wrong reasons. Being "huge" makes it not depend on third parties, which is one of the unique features of Bitcoin.
I use both Bitcoin Core and Electrum, they both have some benefits.