Your mighty armada should include a fleet of fast constructors.
Simply build a string of supply bases to the enemy moving your fleets along with the constructors. Because you only need a supply base at the end of the road to be able to operate there and to send reinforcements there, the starbases in between don't matter after you get your fleets across. If the enemy wants to blow them up it doesn't matter. Similarly, you only need one bridgehead to secure the operation so as long as your fleets are capable of taking one enemy planet "over there" and hold it, all the supply starbases you built to get there can be counted as expendable.
Real armies use pioneers and logistics vehicles, too. The same principle works in GC3, too.