I've blown up a bike tire at a gas station. Long time ago. I was a rookie.

I think the problem is the volume of air that comes out in such a quick space of time. A car tire may need lower pressures than a bike tire, but a bike tire fills much, much quicker because of the smaller tube.

I bought a quality floor pump somewhere about 10 to 15 years ago and it's still working great, so the expense was easily worth it.