Note that a lot of the answer to this question hinges on what you mean by "infect". Bdellovibrios (as Laurel has already established that this does happen) do something that does look a lot like infecting eukaryotic cells- but it is still spoken of as "hunting". Why? I am not sure.
There are lots of different ways that bacteria can have negative interactions with each other- though they often resemble "hunting" or "warfare" more than "infection".
Getting a bit more into the "how" of the question, a common mechanism for inter-bacterial negative interaction is the Type VI secretion system. This apparatus is often spoken of as a "weapon" that bacteria can use to kill each other, by adhering to the other cell and shooting toxins in through its membrane. They can use this to great ecological effect.
The type VI secretion system is also used in some contexts for infecting non-bacterial hosts, so by that logic you could argue that it resembles infection.
Update: for a short discussion of inter-bacterial killing (including Bdellovibrio + secretion systems) in the context of biotechnological applications, see here.