If Bitcoins aren't tied to a conventional currency, how did they get so valuable?
It's quite the opposite - it's because bitcoin is a decentralised and independent currency that it's got intrinsic value. Its supply can't be modified like fiat can essentially be printed into existence by the government/central bank.
Bitcoin's utility as a decentralised currency is what makes it valuable. People know that it's an international medium of exchange that has a decentralised supply, which means that it's a great long term store of value. That's where the demand comes from. Same principle as gold and silver.
On the contrary, fiat currencies are actually intrinsically worthless - its supply can be increased at any time by a central entity, and we see this with Venezuela and and Zimbabwe as recent examples.