How do you put a shield or bubble on your corps command center?

The bubble you see around some corps commands is temporary and disappears a certain period of time after the corps command is built or rebuilt. I suspect it is intended to prevent someone from tearing your corps command down as soon as it is placed/built.

Use an aegis from your items

You don't. The corps command center is the "base" that establishes a Perimeter and you get your buffs from it. The only really way to defend it it is to complete the technology and upgrade it to level 5 so the corps guard number is large. You may occupy it as well. So you can stash troops in it while your personal command center is shielded. If enough people reinforce the corps command and depending on the quality of the troops it may take 1 to maybe multiple rallies to get it to the point where there are no troops and it can be destroyed.