That is not a bed bug. The picture is rather poor, which makes an ID difficult, but I think it might be the beetle Ptinus fur (spider beetle), or another species from the same genus. This species is found all over the world, and often indoors (they can e.g. feed on dry foods).
Reasons for this suggestion is the body shape (incl relatively hidden head), color ("reddish"),long legs with thick femurs, long hind legs, and long antenna. The long legs together with the long antenna (the antenna can look similar to a fourth set of legs), as well as the hidden head (so the body look two-segmented) is what makes it look somewhat like a spider .
(picture from bugguide.net)