Would an object like a wooden bed interfere or block the signal coming from a 802.11 wireless router?
The question is about physics, but not in terms easily answerable by a physicist.
In general, yes there will be some dampening, depending on the factors above.
WiFi signals are just microwaves, so they are affected by the same things. If something would prevent a microwave oven from working, there is a good chance it will also block a wireless signal.
In case of a wooden bed, humidity in the wood could reduce the signal, although not by much. Even if wood would absorb microwaves, a bed is typically not a massive slab of it, but has openings between the slats etc.. You would more likely get an effect from any springs in the matress. Other things that commonly weaken the signal are steel in reenforced concrete walls, and anti-glare coatings on windows.
This would be a great case for an experiment btw..