FWIW, I am not a good bughouse player, but that may be more due to my poor blitz play.
It is better to be aggressive and attack in Bughouse, If you are attacking on both boards, you will likely win, and yet, both white and black have to be concerned with defense, as dropped pieces can start an attack out of thin air. The best defense is a good offense even more so in Bughouse.
Dropped pieces, sacrifices to draw the king out, and dropped pawn chains are the usual modes of attack. The six squares a knights move from your king, the back rank, and the f7 (f2 for white) are the key squares to occupy and guard.
Squares are more important than lines in Bughouse. Lines are easily blocked by dropped pieces and squares are easily used by blocked pieces.
Development is important in Bughouse like regular chess, both for attack and defense. Your pieces on the board are your first line of defense against dropped pieces.
You want to move as few pawns off their starting squares as possible, and try to play with pieces. Pawns on the attack are usually dropped.
Piece values are quite different than regular chess. Pawns are more important and long distance pieces less. Also, the values are even more dependent on the board position than in regular chess. I would give as an approximation P-1, B-2, R-2, N-2.5, Q-5
A piece in the hand is worth two on the board.