When the bacteria eat the uranium, what it's really doing is oxidizing it (burning it if you will), and the excreting it. That uranium oxide is then just sitting there.

It might then decay, and if it does it will emit the radiation. The process of being eating, and/or oxidized changes nothing whatsoever about the uranium decaying, it will do so, at a random, unpredictable time, and nothing you can do to it will speed that up or slow it down.

A bit more about radiation: When uranium decays it can emit various thing, those things are collectively called "radiation". Those things also exist on their own (created in other ways), and when they do they get a new name.

So radiation can be thought of as "the process of emitting something, while an atom decays", it's a process, not a thing in and of itself. i.e. since it's not a thing, it can't be incorporated into the bacteria in the way you are asking.

Most of the emitted radiation is traveling way too fast to be incorporated into the bacteria, it will travel until it crashes into something, damaging that thing in the process (that's what makes it dangerous).

Sometimes (it varies) the exact same particle, not traveling fast, can be useful and/or harmless.

Does that make sense? If not feel free to ask more.