When my dog ate a part of his blanket, my vet said it was very possible it could have been done 3-4 weeks prior to his symptoms. It's just at what point do the pieces clog up those tubes. It depends on what was eaten too, obviously something like a hoof is going to show up faster than small pieces of something (ie rawhide) that can clump together to form a larger "mass" before causing a problem.
So, it really just depends, anywhere from 12 hours to a few weeks is my answer. If you suspect this you need to go to the vet and probably get an x-ray to see what if anything is in there. And in the mean time take all bedding away so it doesn't happen again. My dog almost died from an intestinal blockage, very scary stuff, long recovery time, and very expensive.
Also no reason to just give rice. Typically for a bland diet it's one part chicken to two parts rice (so you can do 1 cup chicken to 2 cups rice). He needs the protein and more nutrition than just plain rice.
Tyson, white, 4 years, Boxer & Thor, 2 year old GSD
Tiger and Raven, kitties, 10 and 11 years
Erin flashy fawn, Lucas, Flashy Fawn, Boxer angels, RIP 11-29-10 and 8-22-07