Various accounts of the battle suggest that makeshift bridges were put in place but that they were inadequate.
Macdonald says that 'Colonel Marion, who commanded the engineers in my army corps, had succeeded in crossing to the other side. He had had two trees cut down and thrown across the river, joining them together with doors, shutters and planks.'
Which shows that it was possible to make bridges at short notice and if they had been prepared in advance they could have been made substantial enough for the troops to cross safely (Marion's bridge had effectively collapsed by the time Macdonald reached it) Had a few bridges been put in place on the second day when there was no significant fighting going on the battle would still have been lost but it would not have been seen as a disaster. The idea that bridge-building would have given away Napoleon's plans is ridiculous - he could have been using bridges to bring up reinforcements or munitions.
How was it Dulaouloy's fault?