Sub for player with blood
 

Wanting to make sure I got this correct.
A3 has a bloody knee, so he is directed to leave by my partner. Coach replaces A3 with A6. Now we are about to make the ball live on the ensuing throw-in, A coach calls a timeout. At this point, can the coach still buy A3 into the game with a timeout?

No. That TO must be requested before the sub comes in. A3 must now sit until the clock runs.

I think it's too late, but I don't have a book in front of me.

If I'm directing A3 to leave the game and before he sends a sub to the table, Coach A says, "Can I call a timeout instead?", then sure, if the problem can be corrected before the end of the timeout, A3 can stay in.

However, after said direction, once A6 reports and is beckoned, now A3 has been replaced and time must run off the clock before A3 can re-enter, regardless of whether Team A takes a timeout or not.

Once the "replacement interval" has started, it's too late for the coach to take the TO to keep the player in the game.

I don't know if FED has any specific guidance on the specifics of how to handle it, but I usually treat it similarly to a DQ'd player. I go to the coach and ask "Do you want a sub or a TO?" If the coach delays, I go to the table and say "start a timer." Once that happens, a sub is required.

I always present the coach with the two options and let them decide. Yesterday we were in the last couple minutes of a close game. I spotted some blood on one of the teams best player, and sent her to her bench. I was Trail opposite the table and her bench was on the other end of the court. The player went over and they got a towel and started to clean the blood. I could tell they were gonna send her back out, and Center wasn't stepping up so I went over there and informed the coach that she needed to take a timeout to keep the player in the game. She took the timeout. Thanks C.