Lots of good advice here, but here's my take on schooling: You don't start with perfection. You don't go up a training scale like a ladder. Keeping that in mind, the contact will probably come and go, the rhythm may be irregular at times, etc. but it will be good for longer and longer until your whole ride will be perfect!
In my lessons I was reminded (way too often
) to shorten my reins. I also wanted my horse to seek the bit, but it has to be there. I made a lot of mistakes with her (I ended up pulling a few times, to see if it would work---what a mistake!) and she never really gave me good extensions. So do go carefully, as it sounds like you're doing. Also sounds like you have a good teacher.