Like all true bugs (bat bugs are Hemiptera, the same order as such familiar sucking insects as Shield Bugs), bat bugs suck their food via tubular mouth-parts. They use this structure, correctly called a rostrum, by inserting it into their host like a hypodermic needle to ingest body fluids. The close-up below shows the rostrum at rest, lying in a groove below the head and prothorax.
It's interesting to note that human bed bugs are thought to be descended from bat bugs, from the days when bats and humans were more closely associated than today. I can imagine Bronze Age or Neolithic people living in huts, with perhaps Brown Long-eared Bats roosting in the rafters and bat bugs gradually adapting to this larger and less difficult host.
If the pictures haven't given you the creeps, then this will: it's an article from the Lancet, which describes a house in Scotland, where a student was being bitten by what were initially thought to be human bed bugs. They turned out to be bat bugs, wandering from a roost above his bedroom. Fortunately for bat conservation, this seems to have been an isolated situation! http://www.morgellons-uk.net/pdf/bats.pdf
My website: http://www.blogger.com/www.plecotus.co.uk