Don't focus on the ground right in front of you either, it appears to move very quickly and gives the illusion of gong even faster. If you look way up the road it doesn't seem to be as fast.
This.
It's a problem for motorcyclists too (I've been riding them for 30+ years). Look all the way up the road as far as you can see.
When you take a turn you want to take the correct line through it. That's marked by the green line in this diagram :
If you take the dark blue early apex line, you have to tighten your line ("turn harder") through the turn, which means that you have to brake. That's a bad idea, both for safety and for going as fast as you are comfortable with. The light blue late apex is safer, since you have to slow down early and can then let the bike coast and pick up speed through the turn.
Do your braking before the turns, not in them. Not only is that faster and safer but it feels more stable as well. Tires have X amount of traction. If you use some for braking, you have less left for cornering.
One way to get used to cornering harder is to pick a downhill turn on a route you do frequently. Once you know it, practice going faster- let off the brakes a little earlier than you are comfortable with. The bike can turn much harder than any of us turn, you just have to make yourself do it. Every time you go through the turn let off the brakes a moment early.