So looks like I found the forum with other people having issues with 10 + Band. I know Microsoft said that there are Bluetooth issues with the current build and using Cortana from the Band will not work. That's why you are receiving the Bluetooth message about make sure it's turned on and nearby. I have the 1020 on build 10052 and I also have the Band. In short, yes, there is a problem with the Band connecting. Here's everything that I've found out:
1) I can't get the Band to stay paired, with one exception. My friend, on a 1520 build 10052 and the Band, had an instance a few days ago (I think Monday) where suddenly the Band was staying connected for about 3-4 hours, but then his phone locked up and rebooted and went back to not staying connected. We have not been able to replicate this and have been working through it to see if we can get it to stay connected again.
2) You can't use Cortana, I think this has to do with the Bluetooth issue Microsoft mentioned not anything to do with the Band staying connected.
3) You can't use the keyboard to reply to texts from the Band (actually you can't use any method to respond to texts). Plus in general you won't receive text messages to your Band. The exception here is that all of these functions worked when it stayed connected on my friend's 1520.
4) I haven't noticed it automatically syncing so I usually just click on the Microsoft Health app in the morning and after work to have it sync everything the Band has gathered during the day/night. The Band still tracks everything just fine.
5) I still receive notifications, emails, facebook notifications, and facebook messages on my Band. But this was only after pretty much resetting everything. As far as I know you have to first go to Microsoft Health and disable every single tile from the Band and save the change. You then have to go into the Privacy Settings (in the phone settings) and every setting that has Microsoft Health listed you need to disable. Then delete the band from your Bluetooth and uninstall Microsoft Health. Reboot your phone and then go back to the store and download Microsoft Health again. Then pair your Band back to your phone and change all of the Privacy Settings back to enabled for Microsoft Health. Then open Microsoft Health and put all of your tiles that you want back onto the Band. This should enable all notifications except for texts which are usually sporadic.
If I find anything more I'll update this post.
UPDATE!!!
At 5:58pm on 5/10/15 for some weird reason my Band is staying fully connected to my 1020. I messed around a lot with it today so I will try to figure out if I can replicate it. If I can then I will include a detailed guide on how to do it. I'll update this post if I lose the solid connection to my Band. This did not stay after a reboot.
SECOND UPDATE
If you are on build 10080 the Band now stays connected. However, you may notice that you don't receive notifications on your Band. Simple fix is to go to the Microsoft Health app->manage tiles. All of the ones that have the edit option click it and turn them to off. Save the changes and then go back through them and change it to on and save again. You should now receive notifications. Also make sure that the Privacy settings are enabled for Microsoft Health in the settings.