From what I've read about bear attacks, you will have the chance to use only one tool if attacked by a bear. Especially if we are talking about grizzlies, attacks happen at close quarters due to surprise encounters. Add to that, grizzly's are capable of running upwards of 55 kph (35 mph).

Personally, I defer to the advice of the experts in the field likes of Stephen Herrero and Tom Smith who advocate that the best defense against such attacks is bear spray; statistically you are more likely to walk away from a bear attack with bear spray as your primary defense tool and that is really what our end goal should be (I know its mine!). For example, Tom Smith stated the following regarding the gun v. spray debate:

What position do bear biologists take in this debate? I can’t speak for others, but after studying more than 600 Alaska bear attacks, I've learned:

• In 72 incidents of people using bear spray to defend themselves against aggressive bears in Alaska, 98% were uninjured, and those that were suffered only minor injuries.
• In 300 incidents where people carried and used firearms for protection against aggressive bears in Alaska, 40% were injured or killed, including 23 fatalities and 16 severely injured persons. Another 48 people suffered lesser injuries.

That said, it is perhaps even more important to understand the preventative measures you can take to avoid such surprises to start with.

Also, here are some additional conversations here at ETS on the topic: Teens mauled by grizzly in survival skills course, Bear attacks vs armed people