The wireless access point you use to browse the internet is not the same wireless technology as Bluetooth, which can be used to connect peripherals to computers. They are both radio waves, but they operate using different protocols on different frequencies. They essentially speak different languages.
Wireless keyboards, etc, can also work via infra-red which doesn't use radio waves at all and requires line of sight between both devices.
Wi-Fi is often referred to as "wireless internet", because that's what
it is most often used for, accessing the internet. When you see people
surfing the web in a cafe, they're probably using Wi-Fi.
Bluetooth technology is in lots of the devices that you already have and can be
used for all sorts of things. It works for both voice–like talking
hands-free on a headset or speakerphone–and data like pictures, music
Having said that I see no reason why someone couldn't bundle the technology with a wireless access point. I had a brief google search for Bluetooth wireless access points, as this is not something I have come across before and wasn't able to find any clear Bluetooth products.
If you have a USB bluetooth "dongle", there is no reason why you couldn't plug into a powered USB hub, or use a USB extension cable to give it some more distance from your computer.
This wouldn't repeat the signal from different locations like a WiFi network though.