The WiFi bill can not specifically show the internet history on the bill instead of only the bill price and DATA Usage. So I don’t think your parents can directly see the Internet History just from the Wifi Bill.
Rather, WiFi is simply a local distribution network. Your home access router (Coax/TV cable, phone/copper pair, or fiber in rare cases) is connected to the ISP via a cabled line, which handles all internet traffic. Normally, your ISP will only consider the amount of traffic generated by this line, and charge you accordingly.
Even though they could (theoretically, and with a lot of effort) determine how many devices are hidden behind the router interface point, that isn’t something they really care about. A router access point would be able to track even illegal uploads (copyright-protected material like movies and music).
Can a WiFi router see your History?
You can see the websites you visited with WiFi administrator access, so your browsing history is not hidden at all. WiFi routers keep logs, so WiFi owners can see what websites they visited. WiFi administrators can view your browsing history and even intercept your private data with a packet sniffer.
Can someone see my Internet History if I used his Wifi Internet?
Your WiFi owner is the only one who can see which websites you visit as well as the things you search on the Internet. An owner of a WiFi network can easily view what websites you were visiting on their network when such a router is deployed. It records your browsing activity and logs your search history too.
How Can I check the Intenet History:
1. First you need to log into your router via your web browser.

2. Than Go to the Advanced or Administration Option (Depends upon your Router Type)

3. Now click on the System option and go to the System Logs:

4. Scroll down to see your router’s history. Filtering log results on some routers allow you to view specific items.

Can I also Check the Deleted History from the Router logs:
It is common for routers not to store history, and ISPs do not make such records available to anyone without a court order. If it’s not in your browser history, your parents will not find the naughty websites you visited. But in the end, I recommend you don’t watch this kind of thing and do not visit adult sites because it can divert your mind and keep you away from your Future Goals and success. So keep yourself away from these things.
Related: Learn How Parents Can Build Discipline in their Kids
Can WiFi Administrator see what sites I visited incognito?
Unfortunately, yes. WiFi owners, like your local Wireless Internet Service Provider, can track your online activities through their servers. You cannot control internet traffic when your browser is in incognito mode.
So Can Parents see Internet History on Wifi Bill?
Do my parents have access to what I look upon the Internet through my router or internet bill? No, Not at all. The only information that will appear on your statement is the device used to access the internet and the amount of data utilized. It will not reveal which websites were visited.