Using the WiFi and Bluetooth on the Uno Rev 2

but now I have to somehow get data to transmit to the Internet

and

What I guess I really need is a Bluetooth connection

are contradictory. Because BT can not connect to the internet. It sounds like you're confused about how data is communicated over wifi and the internet. There are protocols, such as TCP-IP for that. Keep looking at the examples, you will find many different ways of communicating with either your PC or the internet (through your router).

Connecting via wifi, is like establishing a phone call. Protocols are like talking on the phone. It sounds like you've made a call but don't understand how to talk.

That is a huge subject, there are hundreds of ways to do it. Look at a few IOT projects and take hints from those.