How many bikes are sold each year in the state? How much would the revenue buy in transportation infrastructure?
Let's estimate. Say 5000 bikes are sold each year. A bike mechanic I know says he gets more calls to assemble bikes bought on the internet. But let's pretend this does not change.
Now let's estimate the average sales price. Most bikes are sold at places like WalMart, are cheap and poorly made. I will place the average value at $300, even given so many kids bikes are $150.
5000 X $300 = $1.5 million.
Now, you'll need a person to administer the tax. That means make sure it's collected from about a hundred state shops. So deduct $100,000 for that. 
What can you buy for 1.4 million? The intersection at 29th and Willamette was  $800,000 a few years ago. So about 1.4 nice intersections in the whole state.
Negative impacts? Foot in the door for sales taxes? Fewer kids bikes sold? A plan that does almost nothing but might make a good Fox News Story: Kids bikes taxed!