He doesn't literally say "inject bleach" [EDIT: and also doesn't say: "ingest bleach"]. What transpires is this—

Acting DHS undersecretary Bryan:

> We’re also testing disinfectants readily available. We’ve tested bleach, we’ve tested isopropyl alcohol on the virus, specifically in saliva or in respiratory fluids. And I can tell you that bleach will kill the virus in five minutes; isopropyl alcohol will kill the virus in 30 seconds, and that’s with no manipulation, no rubbing — just spraying it on and letting it go. You rub it and it goes away even faster. We’re also looking at other disinfectants, specifically looking at the COVID-19 virus in saliva.

(and also some stuff about UV light killing Covid)

Then, slightly later:

> THE PRESIDENT: Thank you very much. So I asked Bill [Undersecretary Bryan] a question that probably some of you are thinking of, if you’re totally into that world, which I find to be very interesting. So, supposing we hit the body with a tremendous — whether it’s ultraviolet or just very powerful light — and I think you said that that hasn’t been checked, but you’re going to test it. And then I said, supposing you brought the light inside the body, which you can do either through the skin or in some other way, and I think you said you’re going to test that too. It sounds interesting.

> ACTING UNDER SECRETARY BRYAN: We’ll get to the right folks who could.

> THE PRESIDENT: Right. And then I see the disinfectant, where it knocks it out in a minute. One minute. And is there a way we can do something like that, by injection inside or almost a cleaning. Because you see it gets in the lungs and it does a tremendous number on the lungs. So it would be interesting to check that. So, that, you’re going to have to use medical doctors with. But it sounds — it sounds interesting to me.

Then a question about it:

> Q But I — just, can I ask about — the President mentioned the idea of cleaners, like bleach and isopropyl alcohol you mentioned. There’s no scenario that that could be injected into a person, is there? I mean —

> ACTING UNDER SECRETARY BRYAN: No, I’m here to talk about the findings that we had in the study. We won’t do that within that lab and our lab. So —

> THE PRESIDENT: It wouldn’t be through injection. We’re talking about through almost a cleaning, sterilization of an area. Maybe it works, maybe it doesn’t work. But it certainly has a big effect if it’s on a stationary object.

So, I mean... he kinda does, in a completely dumbshit way, suggest we should explore injecting bleach (or maybe isopropyl alcohol? It's always hard to tell WTF the guy's talking about) but then walks it back when actually questioned on it, but then finished by leaving open the idea of exploring... something? "Maybe it works, maybe it doesn't"—maybe fucking what works? Impossible to know. "We're talking about through almost a cleaning" well, yeah, we know that works for, you know, not the inside of people, so... did you or did you not mean trying to get bleach or isopropyl alcohol inside people? Because the first statement clearly meant that, but then you said, not, but now "maybe it works", but what maybe works? And now my head hurts. "Or almost a cleaning". I mean. What?

Anywho, IIRC from watching this when it happened, he does not seem to be making a joke with the initial comment about using tanning beds or household cleaning product injections to fight covid, or whatever the shit he had in mind when he said that craziness.

[EDIT] Though, to be clear, he does not say people ought to go inject or drink bleach. He just suggests he's going to have government scientists look into the idea, which is hilariously stupid but also not as bad as it's sometimes made out to be.