The response to higher gas taxes would have nothing to do with bikes. We'd buy cars with better fuel efficiency, explore alternative engines with lower costs-per-mile, and continue to pay the tax. Until the efficiency gains match the costs of the tax, the rest of the economy would suffer as most people would have less discretionary spending.
You HAVE to get to work, so you're going to eat the tax. And it's regressive, to boot.
Urban people in the U.S. complain a lot about the suburban nature of most of the country, but there is little that can be reasonably done eliminate the suburbs. Most people in this country simply prefer it, and will pay more for their transportation costs to get it. Raising taxes on these people is not going to change their behavior in any meaningful way. A few extra cents, or even an extra half dollar is gas taxes is going to be a lower cost to them than uprooting their life and moving within biking distance.