there is a permenant hole left every time you poke the stopper. it will be fine. if you are worried about it, bake your batch in one bottle, then transfer it over to another sterile vial afterwards.
in all honesty, there is no need to bake your solution in a sterile vial. after all, you are baking it to sterilize it. that takes care of the bottle too. just use whatever size bottle you need and bake without a stopper, then let cool to a temp that won't melt your syringe, draw it up, and transfer it over to the sterile vial.
After too many batches to count and hundreds of injections, I have never had an infection issue using this method. I use 5%ba as well.