You could buy a 220 volt feed pump. They aren't common, but are available.
You could do like a lot of other pump installers and filtration guys do. Use the green/bare ground wire as a neutral. It's a major code violation, but is done all the time unfortunately. By the way, I'm not recommending that, just bringing it to your attention so as to hopefully deter you from doing it.
The other thing you can do; is use a flow switch. Install the switch somewhere in the ingoing pipe to the home near a 115 volt outlet. Use that power to run the feed pump instead of the pressure switch. If you have sprinklers, this is a must do anyway to save overloading the home with chlorine.