To determine the sales tax, we need to calculate 6% of the original bill amount.
The original bill amount is $10.
Sales tax calculation: \[ \text{Sales Tax} = 10 \times 0.06 = 0.60 \]
Thus, the sales tax on the bill is $0.60.
Therefore, the final answer is: \[ \text{Sales Tax} = \text{Rounded to the nearest cent} = \boxed{0.60} \]