I practice my steps without a partner all the time. For some reason, I've noticed there are some ladies that don't like to do this (my wife being one of them).
I think that if you can do your basic steps without a partner, your balance problems will disappear. The reason is simple. You have to maintain balance to do them without a partner because you have nothing to hang onto. You will then find that you dance more confidently with a partner, because you are only relying on the partner for signals. You are doing your own part of the dance.
Also, before you worry too much about getting patterns correct, talk to your instructor about how to properly take a backward step in a smooth dance. There are exercises you can do to get this right, and it's not as simple as you might think. If he/she says there's nothing special in going backward, IMMEDIATELY find another instructor. If they say you are not ready, I disagree, but I will have to defer to their judgement. I don't think it's ever too early to learn the basics.
Once you can go up and down the ballroom floor backwards, effortlessly, the rest will be a cake walk...OK...it won't...but getting the backwards stuff down will make the rest easier.