How can you save a bool value or something with datastore?

It is not being saved because you are changing the value on the client, and the server doesn't see the change. What you should do is use a RemoteEvent to change it on the server. Here's how you set it up:

-- create a RemoteEvent in ReplicatedStorage, and set the name to "changeChoose"

-- this will be the local script

local chooseEvent = game.ReplicatedStorage:WaitForChild("changeChoose")

script.Parent.Text = "Not Pressed Yet!"

script.Parent.MouseButton1Click:Connect(function()
	
	if Choose.Value == false then
		
		script.Parent.Text = "True"
		chooseEvent:FireServer(true) -- we can use the arguments to our advantage
		
	elseif Choose.Value == true then
		
		script.Parent.Text = "False"
		chooseEvent:FireServer(false)
		
	end
	
end)

-- this will be the server script:

local DataStore = game:GetService("DataStoreService")
local GetData = DataStore:GetDataStore("ValueDataStore")
local Choose = game.ReplicatedStorage.Choose
local chooseEvent = game.ReplicatedStorage.changeChoose

game.Players.PlayerAdded:Connect(function(player)
	
	local data  
	
	local Success,error  = pcall(function()
		
		data = GetData:GetAsync(player.UserId) -- you should only make data something AFTER the pcall
		
	end)
	
	if Success then
		
		Choose.Value = data
		
	else
		
		warn(error)
		
	end
	
end)


game.Players.PlayerRemoving:Connect(function(player)
	
	GetData:SetAsync(player.UserId,Choose.Value)

	-- removed this pcall because it is literally unnessary
	
end)

-- now for our remote event

chooseEvent.OnServerEvent:Connect(function(player,status) -- first argument is always the player, then the arguments we passed on the local script
	
	Choose.Value = status -- since status is false or true, we can set the value to it
	
end)

Remember exploiters can fire the remote and change it to false or true whenever they want, so depending on what you're doing you will be able to secure the remote. Edit: it was saying SetAsync was not a valid member of DataStoreService because you have to do it on the actual datastore, not the service. I've fixed the script.