Votes. 0. Edit Answer (for another -17 minute). The average labor cost to install a bathroom sink faucet runs between $140 to $200 to replace. Since you have three to replace it would probably be on the lower end of the scale and also depends on the complexity of the install.If the sink is in a small vanity that makes it hard to get to it may run higher.otes. 0. Edit Answer (for another -17 minute). The average labor cost to install a bathroom sink faucet runs between $140 to $200 to replace. Since you have three to replace it would probably be on the lower end of the scale and also depends on the complexity of the install.