Low-Power Video Transmission for IoT
Sending streaming video tends to use some resources. I have streamed video on an intel galileo and that used about 0.5 amps.  There is a way to stream without using an OS, but integrating that into your digital system wouldn't be very cohesive.  I have one of these wireless video for my backup camera
eBay backup cam, but the range is not very good. I think you'll need processing on that end with a raspberry pi or something. 

But running this off battery power, you'll want a small solar setup with it. You could have that device on the local network where it feeds the video. I know you said it won't have WIFI, but let's be honest. You're not sending live video over bluetooth. You might be able to send an image or two, but a stream would take some intense coding skills (it is possible but very slow).

As far as the beaglebone goes, look into setting it up as a server. It's pretty simple with raspi, intel galileos but I've never used a beaglebone as a server. From there is where you'll want to send those bluetooth commands to the servo.