What is the highest known bond order?
In the paper that you've mentioned$^{\ast1}$, there is something described, which is called effective bond order ($\mathrm{EBO}$).
$$\mathrm{EBO} = \frac{1}{2}\left(\sum_{i=1}^N \eta_{b,i}-\eta_{a,i}\right)$$
... with $\eta_b = 2 − x$ as the occupation number of an occupied orbital and $\eta_a = x$ as the occupation number of the corresponding antibonding orbital. (In multireference quantum chemistry methods, the resulting averaged orbitals can have occupation values of $0 \leq x \leq 2$)
In 2013 Ruipérez, et al. calculated the effective bond order for several homo- and heteroatomic dimers.$^{\ast2}$ Based on their very high quality calculations, the

[...] results show that the effective bond order ($\mathrm{EBO}$) of the $\ce{MoU}$ dimer (5.5) is higher than that for the tungsten dimer (5.2), known to date as the molecule with the highest $\mathrm{EBO}$.

So somewhat arbitrarily, $\ce{MoU}$ seems to be one of the best candidates for the highest bond order.

References:
$^{\ast1}$. Björn O. Roos, Antonio C. Borin, Laura Gagliardi, &quot;Reaching the Maximum Multiplicity of the Covalent Chemical Bond,&quot; Angew. Chem. Int. Ed. 2007, 46(9), 1469–1472 (https://doi.org/10.1002/anie.200603600).
$^{\ast2}$. Fernando Ruipérez, Gabriel Merino, Jesus M. Ugalde, Ivan Infante, &quot;Molecules with High Bond Orders and Ultrashort Bond Lengths: $\ce{CrU, MoU,}$ and $\ce{WU}$,&quot; Inorg. Chem. 2013, 52(6), 2838–2843 (https://doi.org/10.1021/ic301657c).