Can entropy increase during bond formation?
I do not think that an entropy decrease is a requirement to form a bond.

Think about a "normal" case: $\ce{HCl}$ (a gas) and $\ce{NH3}$ (another gas) react together to form $\ce{NH4Cl}$, which is a solid. This is an example of bond formation where entropy clearly decreases.

But now think what would happen if two liquid or solid compounds react together to form a gaseous compound. An increase of entropy has taken place. Can't think of a concrete example, but I think this might be the case of, for example, an esterification between a liquid alcohol and a liquid carboxylic acid that form an ester where, due to the lose of $\ce{-OH}$ groups, intermolecular interactions are lower and it can result with the product molecule being more volatile than the original compounds.

It's all about the number of micro states in which the compounds can exist, and gas formation from solids or liquids importantly increases entropy.

(PS: These are just some thoughts, really, I'm no physical-chemist.)