Realistically you should be okay with bacteria. They're actually incredibly resiliant. The liverock that came with my tank was sold as dead rock because it had been out of water for a month or so. Lo and behold, as soon as I added it to the tank, within a few days it was producing nitrate, and I never
saw ammonia after adding food to the tank.
It's still producing nitrate, and now I'm in the everlasting battle against nitrate.
The powerhead and HOB filter will help oxygenate the areas, which should help the aerobic bacteria to break down the ammonia.
Going forward, I would only use distilled water from the grocery store (or RO/DI is better, but not easy to find, apparently any in-store water filling container thing is supposed to be an RO/DI unit, so maybe you can find one of those). Don't use spring water, they're just as bad as city water for different reasons.
You can try buying more bacteria, but really just with a powerhead and HOB filter you should be okay, and again I'm pretty sure some bacteria survived. If you live near an LFS, you can ask for a small piece of rock, and maybe some sand, and buy those (should be less than $20, which is less than "bacteria in a bottle") and they'll be better for your tank than bottles.
Now I think you're kind of stuck waiting even longer. I wish there were a consensus or a good thread on ammonia dosing to start a tank, but I haven't found many, only a few articles that weren't very thorough. You would have been better off doing it the old fashioned way, or even just buying one rock to seed the tank.
Do a water change with quality water (maybe buy 5 gallons, one of those 4 gallon nutri-seas jugs, or 2 1 gallon containers) from the LFS. That may help