According to the search results, the following Xbox One controller models have Bluetooth capabilities:

• 1537
• 1697
• 1708

However, only the 1708 model has a built-in Bluetooth connection. The 1537 model is easy to spot as it has the words "DAY ONE 2013" embossed on the front, while the 1697 and 1708 models look similar. To differentiate between the two, one can check the section with the Xbox Guide button. If it is the same material as the shoulder triggers, then it is an older 1697 pad. If it is the same plastic as the front of the controller, then it is a 1708 model with Bluetooth capabilities.

In summary, only the Xbox One controller model 1708 has a built-in Bluetooth connection, while the other two models require an adapter to connect via Bluetooth.