Bed bugs are almost the size of dust. Every vaccum will pick
them up - but this begs the question. Most bed bugs, and even larger critters
like fleas, are mostly unaffected by vaccuming. One physician described
the vaccum as a "mobile home for fleas". Bed bugs are probably
small enough to be blown right through the vaccum because the filters are
generally not efficient enough to catch them. Some people place moth balls or
other toxins in their bags to help kill those that are still in the machines,
but this is not effective too much.
Some vaccums (HEPA rated) may have better success in managing these populations, but you probably have to dispose of the bags or they will eventually crawl back out.
In a regular vaccum cleaner especially with the motor behind the bag they probably could collect in the bag then escape. In the other vaccums they might not survive for two reasons. Assuming they got into the bin, the inner cyclone for fine dust is going at 500MPH. Would'nt the wind velocity kill the bed bugs? Even if they somehow were not sucked out at that point and blew to the filter, the HEPA filter gets very warm when being used, the heat probably would be hot enough to kill the bed bugs if they made it that far.
The only bed bugs that a vacuum cleaner is likely to pick up are the dead ones. This may not be true with a wet vacuum cleaner or a steam cleaner (the latter can clearly kill them). HEPA filters ought to trap most of the bed bugs allergens. On the general matter of choosing a vacuum cleaner, the filtration is important, but most importantly (unless you are considering the steam cleaner), is going for more powerfull vaccum cleaner.
Don't be fooled by all of the claims of bed bugs removal. The truth of the matter is that no vacuum cleaner gets all of the stuff out of your carpet. The most powerful commercial machines get most of it but not all of it. Also, it is the feces of the bed bugs that irritate human beings. If you have severe allergies to the stuff in your carpet you probably should not have carpet at all.
More ways to Kill Bed Bugs