Short answer: no, your detailed search history and exact URLs do not show up on a normal Wi‑Fi/ISP bill. The bill usually only shows:
- Total data used (GB)
- Billing period
- Maybe device limits or speed tier
However, whoever controls the router or network (parents/landlords) could see more if they:
- Log into the router and check logs
- Use monitoring software or a custom DNS service
- Install something directly on your device
Using HTTPS sites (most modern sites) means they can see the domain (e.g., google.com, youtube.com) but not the exact pages or searches via simple network tools. For more privacy, use your own device, strong passwords on accounts, and avoid using networks you don’t trust for sensitive stuff.
Spynger: a parental monitoring app, but that’s something installed on the device, not visible on the Wi‑Fi bill.