Nope, the only way to trade in dollar values is to trade it in dollars. Usually this means USDT (which is not USD, but a crypto tethered to USD.. lots of distrust going around it currently). Bittrex lists only a handful of coins in USDT.

The way I do it is that I keep an eye on coinmarketcap.com and write down the dollar amounts when I buy. It's not perfect, but it's something. Unfortunately the Bitcoin price makes everything look like it's going down, but really Bitcoin is just going up a lot.

The fact everything is traded in Bitcoin is also the reason why Bitcoin is valued so much by the way. It is like how dollars are worth a lot because that is what oil is sold in, Bitcoin is worth a lot because that's what you use to buy other crypto. Oftentimes you can also trade in Ethereum, by the way.