Interesting ionization of sulfuric acid
From what I have learned about oxoacids, the bond strength determines the strength of the acid.


Yes. But that is not the whole picture. You also have to consider what else is floating around in the solution.

The reaction of the species (I assume aqueous solution) is given below:
$$ \ce{H2SO4 &lt;=&gt; HSO4- + H+ &lt;=&gt; SO4^{2-} + 2H+} $$

As you can clearly see, the concentration of the protons is raised when going from left to right. There is a natural equilibrium that pushes backwards.

However, as you correctly point out, the bond stability (or "strength") directly correlates to the stability of the acid species. It might well be (and I'd even bet on it) that the bond strength of $\ce{H-SO4-}$ is higher than $\ce{H-HSO4}$ (note that the bonds indicated here are not the real bonds as they occur but merely a representation) but this requires an in-depth (possibly computational) analysis, as a quick search of the internet did not yield any useful results.



Edit: I did some small, very basic geometry optimization calculations with turbomole (on default settings, so def-SV(P) basis set for all atoms) to find out the bond length of the hydrogen to its oxygen. Turns out my hunch was right, the bond is shorter in $\ce{HSO4-}$ (95.07 pm) than in $\ce{H2SO4}$ (95.72 pm), indicating stronger bonding once the first proton went flying away.