When I have had the opportunity to go driving totally en femme which includes wig and light makeup I've avoided the Interstate and main arterials. On the Interstate you're stuck between the off ramps and, if something does go wrong with your car the chances of getting caught in the headlights is great and having someone stop to help. On the main arterials in my small city it is the same. Too many cars and lights. The neighborhood streets are 25 mph and only have residents living in houses. The chances of collision is reduced. And, if the car does malfunction it is easy to change into my male clothes and wipe off the lip gloss. And, if the car cannot be readily fixed, it is easy to walk home or take public transportation and come back later.
I like strolling in the evening before it gets to late, but, late enough the commuters are already home. I find it is great to walk in a light rain using an umbrella to obscure my obvious male face. There are less casual walkers out when it is raining also.
As to an encounter with the police I am not a drinker, but, I would recommend definitely being 100% alcohol free. In Washington State the law protects cross dressers as well as gays, lesbians and all transgenders from discrimination. The police have no legal right to harass anyone because they are wearing a dress. And, if a cross dressers is picked on by the local populace because she is presenting en femme that qualifies as a hate crime.
Just be careful to minimize breakdowns and definitely choose places to drive that minimize uinintended encounters.