I agree with Speed Racer's comments.
You took a few lessons from her - she wasn't reliable - you moved on. Since you paid for the lessons, you deserve to get them - since you bought a horse, she should give the lessons to you on your horse so that you can get the most benefit from them.
It's the instructors job to stay in contact - if they don't stay in contact or provide the services you pay for - you owe them nothing.
Actually - if you want to get technical - even if you do have a good, long-standing relationship with an instructor, it is still a business relationship and it would be your personal choice to buy a horse, with or without the instructor's permission or input. Part of being an instructor is simply accommodating clients choices and advising them when applicable.
I'd ridden with the same instructor for three years and worked at her barn part time when I bought my gelding completely AGAINST her advice. She didn't like the horse, I absolutely clicked with him and felt he was THE ONE. She shrugged, said 'if that's what you want - it's your money and your neck on a very green 2yr old' - and then with minimal flinching, she loaded him into her trailer, hauled him back the barn, stuffed him into a stall amongst a barnful of her precious chosen babies and on we went with life. She never did much care for the horse, but even she eventually had to admit it was a personal preference issue - her barn logo was on him, she taught me on him and she didn't have any issue hanging ribbons he won on her trailer along with the ribbons earned by the horses she had hand picked.
If this instructor is going to come to your new barn to give you the lessons, check with the barn owner to make sure it is okay before she shows up - just explain that you had already paid for them and would kind of like to see something for your money.