Will the continuing decline of petrol prices result in a proportional decline of Bus and Taxi fares? If not why not?

Not proportionally and probably not at all over the short run.

What is driving the current decline in petrol pricing is the fall in the price of oil. This drop is primarily due to increased supplies by traditional suppliers of oil, seeking to cause negative returns on investment to the competitors who had been able to earn profits extracting oil from tar sands and other more expensive processes. This is a short term effort, and if successful, it will actually cause the price of oil to increase when the market prices in the risk of this as an effective method of reducing supply.

No.

In addition to fuel costs, there are the labor costs for the driver, the maintenance costs for the vehicles and the capital costs in acquiring the vehicles

Then prices are regulated by the cities in which buses and cabs operate. Cities are not particularly responsible in responding to market forces.

Lower gas prices will not increase the number of cabs on the road. The supply of cabs and buses is pretty much fixed.

NO; When fuel prices are down, that means the economy is at a low point !

price and wage are sticky. They are subject to institutional factors, such as contracts.