I'm confused with how to properly use Super Buddies Forever properly. Does adjacency need to be maintained for the +1 attack modification? If I have Charge or Running Shot (just as examples) and start adjacent to Booste & Beetle, would I lose the +1 attack once I move away?

Here's the power:

Many thanks in advance for any help here!

They must remain adjacent. However, if you ENDED Charge or Running Shot next to them, you get the bonus.

This is correct.
The bonus only applies while adjacent.