In a corner, the inside handlebar should be further away, not closer. In any event, the actual movement of the bars is minute.
What you are describing is a lack of confidence in your ability, and I would always recommend advanced rider training for things like this. Apart from teaching you new skills, or enhancing old ones, the training course are a great deal of fun.
Say what?
The inside handlebar is further only during the period to initiate the turn, once in the turn the inside handle
must be closer. You couldn't make a left hand turn for very long without falling over if your handle bars are pointed any amount to the right.
This is not correct.
The bar moves away to initiate the turn, then back towards neutral to maintain the angle. If it moved back towards the rider you would be initiating a turn the other way, or straightening up the line.
Edit:
I'm going to expand on this because I know it is tricky to get your head around, and I struggled with it despite the fact that we ALL do this instinctively.
Okay ... With decent tires and the bike upright, and straight and level, it will run in a straight line until you stop. In order to initiate the turn you have to make the bike behave not like a cylinder (two wheels straight up), but more like a cone. Roll a conical shape on a flat surface and it will roll in circles ... we can all visualize that easily.
When you want to turn left, the dynamics of making the cone mean you have to push the left bar forwards. That points the front wheel right, but you don't go right because the bike "falls over" to the left. That initiates the turn.
What you do next is "stop the turn" radius decreasing. If you kept the same pressure the bike would either fall left, or turn in decreasing radius circles until it hit the ground. So the bar moves slightly back towards the rider just enough to maintain the constant radius you initiated.
Remember a body in motion will remain in constant motion unless you do something to change it. So the bar comes back just a little and you "feather" it to match the radius you want.
If the bar comes back too far, the bike sits up and tries to increase the radius of the turn until finally it is straight and upright again.
If at any time the left bar comes back BEYOND the neutral position, you are then initiating a turn to the right. Effectively you have made a cone sloping the other way. So in a left turn, the left bar is never closer to the rider than it would be in straight and level riding.
I dunno if that is clear as mud, or a decent explanation. In practise we do all this without much conscious thought, and the picture can be complicated by shifting your weight, road cambers, etc. Yet the theory remains sound. We push the left bar to go left, and push the right bar to go right. Getting it straight in your head allows some very rapid direction changes.
Next time you are on a quiet interstate try it. Get up to 70 mph. then use your "push" technique to slalom the white lane dividing lines. You can swerve rapidly and in total control even at high speeds. If you start with small movements you can quite easily build up to rapid changes in direction with complete confidence. Useful when that deer appears in front of you.