My guess is that, when Robert made his move north to link up with Ned Stark and Jon Arryn, he split up his forces – partially to obscure which detachment he was travelling and get the royal forces to split their forces to chase each detachment, partially to make it easier for each detachment to move quickly and to live off the land, and partially because he couldn’t be sure where Ned Stark and Jon Arryn were.
Robert seems to have stopped at Stoney Sept for medical treatment, trusting in the people of the town to keep him secret and safe, and either word got out or Jon Connington got lucky.
As for the Trident, my guess is that Ned and Jon Arryn had already linked up, but had kept their infantry at the crossroads while they rode hard for Riverrun and then for Stoney Sept to bring the Tullys into the fold and to save Robert. After recovering from the Battle of the Bells and waiting for Robert’s forces to coalesce, they marched north to combine their forces for the final battle.
I dunno, what do you think, @warsofasoiaf?