I am now aware that Picasso made it first thanks to it being pointed out to me several times, I am sure he wouldn't mind people making their own versions and recycling dead bikes!
You will need:
Used inner tubes.
Step 1: Get some old handle bars and saddles.
Step 2: Match Up the Handlebars and Saddles to Make Cool Horned Skull Shapes.
Play around with making different pairs of handle bars and saddles until you get some good looking bull-like horned skull shapes.
Step 3: Fasten the Horns to the Saddles.
This makes them pretty secure, strong enough to hang coats or helmets off of, for example. I have seen some bike taxidermy wall hooks used to hang bikes from, but I am assuming that the handle bars are welded together.
Step 4: Reinforce Cableties by Wrapping the Joins in Inner tubes.
I think hiding the cable ties is good, as it looks like it's all completely made out of dead bike bits, and it does give the fastenings a bit more strength. There will still be some movement in the handlebars though, that's why I'm not going to try and hang anything too heavy off the finished pieces.
Step 5: Make the Trophy Mount from Hardboard.
I wasn't too precious about the accuracy of the trophy shape, keeping the rusty d.i.y. wonkey vibe, I think it adds to the dead bike feel.
I made a rough template and drew it on the hardboard and cut it out with a jigsaw. I'm sure there's lots of Instructables about how to use jigsaws if you need that info.