You've been listening to a lot of propaganda to believe that. The only country that bans women from driving is Saudi Arabia, and that is far from the only country that applies sharia. Sure, highly conservative Muslims will seek to deny women those rights, but that's based on the same kind of distorted readings as SCOTUS once claiming that African Americans could not be US citizens.
The prophet Mohamed said : "Seeking knowledge is an obligation upon every Muslim".
there's another hadith that I wanted to post but I couldn't remember it, where the prophet talks about a time a couple of years after him where there will be peace to the point woman can travel a cross the desert on a camel alone, and this truly happened, if Islam had problem with woman traveling alone, he wouldn't mention this, there's a lot of things that people associate with Islam that has nothing to do with Islam, there's plenty of Muslim countries, and they are all different.