Is there to simplify this script?

Actually, the issues here are minimal, good job! First of all, I don't know if this could be simplified... I know of a couple of different ways it could be written, but I wouldn't say they are simpler or better, just different.

To fix this, there's two things you need to do.

Fix the Exploit:

What's happening is when the player presses the key again, the script starts another while loop which increases the speed at which it recharges. All you need to do, is put the entire Key up function inside a checker so it can't start if it's already started.

Fix the server not working:

Even easier. The problem is the script loads before the other things needed load; specifically bool. You need to do WaitForChild at the beginning so the script doesn't start until bool loads.

I applied these changes; here's the result. (I also made a couple of other changes to help the efficiency of the script; I hope that's ok. I believe it works the way you intended. If you want to force the player to wait for it to recharge each time, uncomment the marked lines; also, you don't really need the NumberValue called Value)

script:WaitForChild("Bool")

MyMouse = game.Players.LocalPlayer:GetMouse()
Player = game.Players.LocalPlayer

local xSize = 1
local speed = 0.01
local human = Player.Character.Humanoid
--local human = Player.Character:FindFirstChild("Humanoid")
--script.Parent.Parent.Parent.Parent.Character.Humanoid

MyMouse.KeyDown:connect(function(key)
	if (key:byte() == 48) then
		script.Bool.Value = true
				
		--if xSize ~= 1 then
		--	script.Bool.Value = false--------Uncomment this section to force the player to recharge fully before use again
		--end
		
		while script.Bool.Value == true do
			if xSize > 0.01 then
				human.WalkSpeed = 100
				xSize = xSize - speed
				wait()
				script.Parent.Bar.Size = UDim2.new(xSize,0,1,0)
			end
			if xSize <= 0.01 then
				human.WalkSpeed = 16
				break
			end
		end
	end
end)

MyMouse.KeyUp:connect(function(key)
	if script.Bool.Value == true then
		if (key:byte() == 48) then
			human.WalkSpeed = 16
			script.Bool.Value = false
			while script.Bool.Value == false do
				if xSize < 1 then
					xSize = xSize + speed
					wait()
					script.Parent.Bar.Size = UDim2.new(xSize,0,1,0)
				else
					wait()
					break
				end
			end
		end
	end
end)