Step 1: Recall the structure of diborane.
Diborane is $B_2H_6$. It has two kinds of bonds. Four hydrogens are normal terminal bonds and two hydrogens form special bridge bonds between the two boron atoms.
Step 2: Understand the bridge bond.
A bridge bond is a three-centre two-electron bond. This means three atoms, $B-H-B$, share just one pair of electrons. It is also called a banana bond.
Step 3: Count the bridge bonds.
In diborane there are exactly two of these $B-H-B$ bridge bonds.
Step 4: Count electrons per bridge.
Each three-centre bridge bond holds one pair, which is 2 electrons.
Step 5: Find the total.
Multiply the number of bridges by electrons per bridge. \[ 2 \text{ bridges} \times 2 \text{ electrons} = 4 \text{ electrons} \]
Step 6: State the answer.
So the total number of electrons in the bridge bonds is 4. \[ \boxed{4} \]