Bittrex does not have an option to let you deposit fiat currency. Not sure if/when they will add that feature. Bittrex is an exchange where you can trade/exchange altcoins. It also has wallets to store altcoins. Keep in mind that Bittrex has a higher withdrawal/transfer fee compared to Binance (another exchange).
If you want to buy bitcoin with fiat currency, sign up with Coinbase (CB). Then deposit fiat currency into your CB account using a bank account. Note that depositing takes about a week with no fee. You can also do a bank wire transfer which takes 2-3 days, but you will be charged a $10.00 fee by CB and some fee by your bank.
Thanks and good luck.