Dunno about Bittrex but Kraken also has a USD/USDT pair. Withdrawals via wire transfer take around 2 days.

I have not had problems with them, but I'm also not doing any large transactions.

Also note Kraken, withdrawals are as fast as a wire transfer (so a few days): https://www.kraken.com/en-us/prices/usdt-tether-usd-price-ch...

What I'm not sure is how that market connects to Tether's bank accounts increasing or decreasing in holdings. This is all third-party exchanges, presumably with other customers as the counterparty.