In all, Bing is fast and accurate, with lots of sophisticated options. If it were the first Internet search service you’d ever tried, you’d probably never quit. Unfortunately for Microsoft, Google got to us first, and after all these years it feels so much like home that most of us have no reason to leave.
That's called First Mover Advantage, the advantage gained by the initial ("first-moving") significant occupant of a market segment. Although Google was not the first search engine, but it was the most technologically advanced and it was able to garner the biggest share of the search market. And with the kind of share Google has, there comes inherent network effects which causes the value of a service to increase for a new consumer based on the number of people already using the service. Google being smart has used the Network effects to understand what people are doing using Google and then improving the service continuously.
Bing although a very good alternative lacks the Network effects and thus the increase in search share so tough for Bing. So what does Bing need to do - Continuously innovate, improve its algorithm, add new services, market itself suitably and spend money to acquire enough traffic to generate network effects for itself. It will be a long walk but remember switching costs for online services are very low. Typing a new address in your browser or changing search defaults is as easy as it gets to switch.
Bing needs a chance and that is the biggest challenge for it. How to get enough people to try it and realize that it does what Google does, somethings even better.