I'm a firm believer that you don't need to change your style too much in order to make it bike friendly. A lot of people are afraid that they'll have to sacrifice their style in order to ride regularly, or make biking their main mode of transportation. In some cases this can be true. If you have a big commute you'll have to factor in getting hot and sweaty, and if you ride all year round and when it's raining that's another consideration, since you don't want to be soaking wet when you arrive at your destination. But for more low-key, around-town riding, you shouldn't have to change your style too much. If you like wearing skirts and dresses, don't worry! There are ways to make your outfits bike-friendly so you can keep wearing the dresses you love wearing.
If it's not too hot out, consider wearing opaque tights. I like wearing tights when I ride because in my mind I'm essentially wearing pants or leggings. If my skirt flies up a bit, it's not like I'll be flashing anyone because you're just getting a glimpse of more tights.
Avoid wearing tight skirts, like bodycon skirts. Sometimes you can make it work, but it's way harder to pedal when your skirt is binding your legs together. Longer, knee-length skirts that aren't very tight are much easier to pedal in, because the fabric allows a lot of freedom to move.
If you opt for a longer maxi skirt, make sure you keep it from getting caught up in your gears or back tire. If you have a longer, flowy skirt you can tie it up into a knot while you're riding to keep the excess fabric from getting stuck in the bike's moving parts, and you can untie the skirt when you've arrived.
If you're afraid of your skirt flying up and it's too warm for tights, wear some bike shorts! As long as your skirt isn't too short, you won't see it unless your skirt flies up a bit while riding.
Tuck! I like to sit on my skirt, and then some times I tuck my skirt under my legs to keep it from flying around. If I'm sitting on my skirt then it can't fly up and flash anyone.
And I think that confidence also can be super helpful when it comes to wearing skirts and biking. You might get people hollering at you or commenting (I swear, people have a weird sense of what's appropriate to say to bike riders), but if you can just ignore any weird comments, that goes a long way. I've had people holler at me when I was wearing something totally modest and also when I was wearing a shorter skirt with no tights, so it doesn't have as much to do with what you're wearing as it does with the person yelling at you being weird and inappropriate. But, if that kind of stuff does bother you, wearing tights or bike shorts can be a nice way to feel more modest. Nobody should make you feel bad for what you are wearing, and just because you're on a bike shouldn't be a good reason for disparaging or weird comments on your clothes. I wear heels and bike quite frequently and have had people comment on that before. I know that I can bike just fine in heels and only wear shoes which I feel are safe and comfortable to bike it. So wear your biking outfits with confidence!