Please notice that:
The first letter of Just and She must be capital because of full stop and exclamation mark.
You may also say:
My cultured teacher is almost 10 years older than me, so, I can hardly keep in touch and talk with her.
But she is delighted when you step forward and give her a rose , it is an effective step to be more friendly, and then let your cultured teacher know you are cultured too.