Is it possible to see if player exchanging bushes is on another team?

If you are president or officer and your team has a vacancy, then you can. Tap on you club icon. Below the member list, tap on the icon with a green "+" sign. This should bring up everyone on your member list. If the player has a green button, they are not on a team and can be invited. If they have a gray checkmark, they are already on a team. The game will tell you so, if you tap on the checkmark.

BTW, if you team is full, everyone on the list will have a gray checkmark, whether they are on a team or not. If you tap on any of these checkmarks, it will say, "Your club is already full."