That is exactly what IIR seekers do, like one on python 5 AAM or NSM antiship missile. As for what does a stealth bomber look like... well, it would depend on the sensitivy of the sensor, on the IR signature of the target and the distance between the two. Sadly, there is no way you can get a precise answer to that question here or anywhere outside of the users of the said bomber. IR signature would also depend on the angle we're looking at the bomber, and the power of its engines at that moment. Also, temperature of the surrounding air and ground can come into play.
all in all, and this is just a guesstimate, i would doubt a bomber like b2 could be detected head on at over 20-30 or so km. It being nighttime bomber would also make it harder to positively indentify it in the nighttime from said distance. It would just be a blip from that distance, you'd have to get even closer to see the actual shape that heat is making.
Of course, in the daytime, it'd be somewhat eeasier. I do believe today's tech allows for very fast scanning of the skies, and zooming the camera on sevaral potential IR blips on the horizon in reasonably short period of the time. Having a database of all the possible targets, from all the possible angles and distances would help you identify the blip and its approximate distance from you.
So... yes, it's possible to deal with b2 like that. But you'd have to have a fair number of planes in the air, covering the area. And b2 would have to be alone. Against f22, even in the daytime, i just don't know how that'd work. At best, you could sacrifice enough planes so enemy runs out of missiles and has to abort the mission early. But that's not a tactic to be used repeatedly.
