As of Gen 4, sleep status will cancel Bide. Patrat's attack would not go through. The Pokemon will therefore be able to choose a different move to use, since the Bide status was cancelled. However, prior to Gen 4, sleep would merely pause the Bide, which would continue after the Pokemon wakes.
Interestingly, other conditions such as freeze and flinching were not revised in Gen 4, and will not cancel Bide like sleep does. Bulbapedia mentions nothing about full paralysis, nor do other websites I checked for information.