Microsoft did try an experiment of a Bluetooth adapter that attached to the keyboards back in the early days of the Surface line but the adapter did not really work well.
Microsoft does have a foldable Bluetooth keyboard under "Accessories/Keyboards & Mice" on their online Store page but it is not designed to act as a cover for the tablet screen as well.
Microsoft is not too good with Bluetooth and you are best to venture along to look at Belkin, Kensington, and others that make Bluetooth keyboards to see if you can find something with at least some quality to them. Most do not as you have noticed.
It is actually a shame that Microsoft discontinued the "Wedge" keyboard and I have one which works outstanding with just about anything Bluetooth. In fact, it has a rubber cover that when detached, it turns the keyboard on plus the cover can be folded and used as a tablet stand. If you can find one of those somewhere, they worked great.