Begin by securing the 1st and 3rd slides
with twister-ties, pipecleaners, or polybands.

The box is crucial. I use a custom 24" x 8" x 12" double-wall box.

A double-wall box provides much more protection for your instrument.

Put the box together by securely taping the bottom seam.
Then, put the box aside to begin preparing the trumpet.

Place the horn lengthwise on the bubblewrap as shown.

Flip the horn, end over end.

Continue this end over end wrapping.

You'll end up with 5-6 layers of bubblewrap on both sides of the horn.
(You could call it a 10-12 layer stack, with the horn in the center.)

Seal the end of the wrap with tape.

Pinch the wrap together at one end of the horn.

Tape around the bubblewrap,to keep the horn from shifting within the bubblewrapping.

Repeat on the other end.

If you've followed the directions thus far, you'll now have a giant bow tie.

Continue taping by securing the middle.

Tape any additional items (mouthpiece, slides, etc.) onto the outside of the bubble bundle.
Here I have a bottle of 5 Starr valve oil and old springs attached.

I put 2-3 layers of bubblewrap in the bottom of the box.

Put the wrapped horn into the box.

Finish filling the box with another 2-3 layers of bubblewrap, peanuts,
or other void-fill, to completely and tightly fill the box you are using.

Fold in the flaps on top of box, end flaps first.

Putting a piece of tape across the middle
will help hold the box flaps down.

Seal the box top lengthwise with tape.

The Finished Job!
I'd like to thank my packing assistant, Roger.
His shirt references the Marsalis Music artists group, which features recordings by Branford Marsalis and the instrumental works of Harry Connick, Jr.(official site, fan site.)