Given that Bacteria usually reproduce by simply dividing in two and from Encyclopedia.com:" Reproduction is chiefly by binary fission, cell division yielding identical daughter cells. Some bacteria reproduce by budding or fragmentation.", I would say that they reproduce asexually.
Sexuality in bacteria is not tied to reproduction; bacteria transfer genes via plasmids. Do you have any problem with the idea that single-celled organisms can exchange genetic material by comparatively simple means?
Then you are badly misinformed.
They usually fall back on single-cells. You're lucky they're not doing the virus thing.