Mmm, just be careful.. I don't know about everyone else, but I have found that green/"problem horses" are worse if you ride bareback.. Maybe because the riders seat bones dig into their back (which they haven't felt before)? I tried it back in the day for the same reasons as you, but because the horse was even more tense I soon learnt to tackle the issues with the saddle before even thinking about riding.
Just schedule a whole day, and saddle her up as if you were breaking her in. I am talking about going through all the steps as if it was her first time from rubbing her down with the gear all the way to lunging her with the saddle on before you even think about getting on. Only move to the next step when she is relaxed and indifferent to what you are doing in your current step.
This true. Hunter is only 4 and he hates it when I ride bareback. Doesn't help that my balance isn't what it used to be.