In ACOK, after Renly gets shadowbabied, would it have been possible / a good idea for Stannis to go to Bitterbridge personally with all or most of his army to collect Renly’s infantry rather than relying just on Errol Florent and Parmen Crane?

The basic problem is that Stannis would be outnumbered when he got there, because the overwhelming majority of Renly’s army were Reachermen. Even with the Florents and the Fossoways behind him, it would have been a bloody affair with Randyll Tarly in a take-no-prisoners mood. 

And it would mean leaving Storm’s End untaken behind him and giving King’s Landing a lot more time to prepare.