Draven is one of the most mechanically complex ADC's to play, while being wrapped in a relatively simple to grasp kit that can be confusing. If you don't have your axes, you do no damage. If you have your axes, you do a ton of damage. Once you understand that, which you probably already do, you want to try to master controlling where your axes will land, and that's an art all in istself.
As far as laning in general when it comes to bot lane you want to try to look at not only your own minions but the enemy minions. When you balance out the wave to where you have free time between CS and your opponent is forced to grab 1-2 creeps or they miss them, you can force a trade. At that point, they will either take the damage for free, or they will lose CS. Whether you are winning by kills or CS early, a lead is a lead. After first back you should see the spoils of this early lead start to pay off. If you see the support in position for an auto, give it to em with an axe, they'll think twice before getting into your zone of control again.
I feel like the biggest thing to master in every lane outside of being able to farm is having a "presence." You want your enemy to fear you, not think they can walk all over you. For example, if you push early level 1 to get the level 2 advantage (Which you should be doing as Draven), and they are sitting there farming and you have nothing to last hit, chunk them with an axe. I promise they will reposition or waste CD's on you and you should outtrade relatively everyone if they choose to pick an extended fight and you maintain control of your axes. That level 2 powerspike is huge in every lane and even more-so when you're playing a snowball champion like Draven. Your level 6 Powerspike is average, and your 5 is equivalent to the powerspike of pre-nerf Graves (Very strong), so abuse those times in the lane, and punish your opponent whenever you can.
This is a lot to take in, but try to think of it like a boxing match. You want to get free jabs in on your opponent that they cant answer back with. Once you secure a few of those and they're weakened, you can go for your planned all in. Supports play a huge role and as long as you are clear with them and communicate before laning starts "I want to push for two and kill whoever is out of position" they should get the picture. If you are lucky enough to be with a support main they should probably know that already by champ select.
Hope this was helpful for you, and good luck on the rift!