As of 12/12/2017, there is no updated version, either Android or Windows that allows Bither to go beyond the 1mBTC transaction fee. At that transaction fee, it might take forever or never for a transaction to go through.
There is NO direct information on Bither on how to do this, but after nearly a full day of work, i figured out how to derive the Bitcoin private Key from the HDaccount wallet from Windows Bither. It took a bit of reading and trial and error but, i had success.
From Bither, I exported the Seed Phrase. I then utilized the website at https://coinomi.com/recovery-phrase-tool.html.
Instead of trusting the website, even though it's supposedly java client based, i saved the website to an OFF INTERNET computer, and ran the webpage from my offline computer. I put in the seed phrase which then spit out derived bitcoin addresses and private keys.
I was then able to use that private key to access my bitcoin from another software that has better up to date support including transaction fees.
I hope this helps others.