Frodo wasn't going anywhere until the Orcs had passed by!
Movie Frodo didn't behave right either. If he really wanted to give everyone the slip he would have put on the Ring like he did in the book:
"I must go now or I shall never go. I shan't get a chance again. I hate leaving them, and like this without any explanation. But surely they will understand. Sam will. And what else can I do?"Slowly he drew out the Ring and put it on once more. He vanished and passed down the hill, less than a rustle of the wind.
Yeah! I'll agree with you there. I was disappointed we didn't get to see the boat sliding by itself into the river, Sam chasing after it, and the invisible Frodo rescuing him from the river.
Ummm, by this time Frodo realized that wearing the ring drew the attention of Sauron-and others, like black riders; that 'wearing' it was in fact, like wearing a 'magnet', making him visible to forces worse than those he could see.
Don't know, but he had been told not to use it, when he did...he had been wounded...