Over the decades of its existence (the Bureau has its roots in the British Paranormal Society formed in 1877, it became an official organization in 1945), the Bureau of Paranormal Research and Defense (BPRD) has grown somewhat, and remains the foremost agency of its kind in the world. It currently employs between 300 and 350 people, including contractors. Most of them are researchers and scientists, and most of them are normal humans.
The Bureau is a private organization, international in scope, funded primarily by the United States with some money coming from the United Kingdom and other nations. In return, the Bureau handles their paranormal problems. Several of the nations have considered setting up government agencies to replace the BPRD, but the Bureau already has the knowledge, the resources and (perhaps most important) the people. A new agency would essentially have to hire away all the BPRD's experts in order to compete. It's more cost-effective simply to fund the Bureau (and it also provides plausible deniability, when Bureau agents mess up). Nations that do not fund the Bureau still tend to cooperate if the Bureau wishes to perform an investigation in their territory this even extends to nations on unfriendly terms with the United States. In general, this is because the Bureau is very good about sharing information on a completed operation; it also has a history of stamping out problems before theu get truly serious.
The international cooperation depends on the Bureau's public image. That puts the Bureau in the fragile position of being a low-profile organization, with a secret headquarters, that nevertheless is always in the market for good publicity. It also trades very heavily on the prestige of Hellboy and other famous oddities on its staff.