[Sarumian]

I think as well that Saruman considered that the situation had ripened for the decisive blow. Saruman had a formidable army. Having won the battle at the Fords of Izen, he could expect little resistance from anyone but Eomer, who was legally an outcast, was far away and did not have too many men under his command.

Grimma was expelled after the war had already began; thus we can be re-formulate the question -

Why did Saruman decide to move all his force into Rohan having lost his control over king Theoden?

It seems, he correctly estimated that any manpower that Theoden was able to muster would be insufficient to hold against Saruman's army. Therefore everything was in favour of taking a quick, decisive action. He could not expect that:

1. Theoden would be able to hold Hornburg until Eomer returns;
2. He could not expect that Farngorn would come to help Rohan - it was something totally unthinkable.

We also know that Sauron had not prepared to attack Gondor by that time. He was still preoccupied with bringing the army of Minas Morgul up to strength when he discovered a hobbit looking into a Palantir, found out that Izengard had fallen and concluded that the Ring with a hobbit and Aragorn was on the way to Minas Tirith. Pipin's obsession with Palantir resulted in the situation when Sauron launched his assault on Gondor too early and, lost the battle for this reason.

I tend to think, Saruman's position was so tricky that he in fact did not intend to wait for Sauron. In the book (unlike to the movie) Saruman was not Sauron's puppet; he dreamt about obtaining the Ring; he did not allow Witch King into Izengard when the Nine were searching for the Ring and Baggins; as I remember the reason was that began creating his army without Sauron's permission and didn't want to show it as it would have been an evidence of his treachery against Sauron. I believe, Saruman wanted to built up a considerable power base before Sauron could defeat Gondor in order to make a better agreement. May be he expected to be appointed a "viceroy" of the West or North-West (excluding Gondor) at least.