To calculate the price elasticity of demand, we use the formula:

\(E_d = \frac{\%\, \text{Change in Quantity Demanded}}{\%\, \text{Change in Price}}\)

First, calculate the percentage change in quantity demanded:

\(\%\, \text{Change in Quantity Demanded} = \frac{\text{New Quantity} - \text{Old Quantity}}{\text{Old Quantity}} \times 100 = \frac{500 - 300}{300} \times 100 = \frac{200}{300} \times 100 = \frac{2}{3} \times 100 \approx 66.7\%\)

Next, calculate the percentage change in price:

\(\%\, \text{Change in Price} = \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100 = \frac{80 - 120}{120} \times 100 = \frac{-40}{120} \times 100 = -\frac{1}{3} \times 100 = -33.3\%\)

The formula for elasticity is concerned with the absolute values of these changes, so:
\(E_d = \left| \frac{66.7}{33.3} \right| = 2.0\)

Therefore, the price elasticity of demand for the bicycle is 2.0.