OP Wright carried a bullet around in his pocket for a 1/2 hour.
The FBI refused to take it.

Eddie Barker | News Director, KRLD-TV

Wright: I told him to withhold and not to let anyone remove the bullet, and I would get a hold of either Secret Service,
or the FBI and turn it over to them. Thereby, it wouldn't have come through hands at all.
I contacted the FBI and they said they were not interested because it wasn't their responsibility to make investigations.
So I got a hold of a Secret Service man, and they didn't seem interested in coming to look at the bullet in the position it was in then.

So I went back to the area where Mr. Tomlinson was, and picked up the bullet, and put it in my pocket,
and I carried it some 30 or 40 minutes. And I gave it to a Secret Serviceman that was guarding the main door into the emergency room.

Barker: Mr Wright, when you gave this bullet to the Secret Service agent, did he mark it in anyway?
Wright: No, sir.

Barker: What did he do with it?
Wright: Put it in his left hand coat pocket.

Barker: Well now, did he ask your name, or who you were, or any questions at all about the bullet?
Wright: No, sir.

Barker: How did the conversation go? Do you remember?

Wright: I just told him, this was the bullet that was picked up on a stretcher,
that had come off the emergency elevator, that might be involved with the wounding of the Governor Connally.
And I handed him the bullet, and he took it, and looked at, and said, "O.K." and put it in his pocket.

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The memo about a bullet "might be involved with the wounding of the Governor Connally."
The phone call was clarifying what he had told to a secret service agent.

  It is a p--- poor example of the word bullet used to describe fragments
In this case was CE-399

That memo is clearly bullet and fragments.
A bullet mentioned several times

they own the films and will only give them to, say, documentary directors or people in the industry wanting to license the film.