What should I tell her when she asks why bitcoin is better than regular money?
You are convincing the wrong person.
Convince local merchants.
As the number of merchants accepting bitcoins increases, the benefits for the consumer will become self-evident. Until the average consumer sees bitcoin accepted in many of the places they frequent on a daily basis, the vast majority of them won't see a benefit beyond the speculative opportunities.
If you are insistent on convincing your grandmother, you can try pointing out the well published and permanently fixed inflation schedule and eventual supply limit. This ensures that the value that is held in bitcoin can't be arbitrarily reduced by a central bank choosing to inflate the supply with massive printing of additional currency or techniques such as quantitative easing.
You might also point out that (unlike the currency in her purse), she can store backup copies of her bitcoins. This way if her house were to be destroyed (fire, tornado, flood, meteorite, tsunami, earthquake, hurricane, etc.) she would still have access to her bitcoin assets (unlike any hard currency that she may have had stored in the house).
You might point out that the government has been known at times to erroneously freeze or confiscate the wrong financial accounts, and that while this tends to eventually be straightened out, it be a significant source of stress in the life of the individual who temporarily (days? weeks? months?) doesn't have access to their financial assets to pay for their daily expenses (food, housing, etc). You can follow that up by pointing out that bitcoins cannot be "confiscated" or "frozen" (accidentally or intentionally) without gaining physical access to ALL backup copies of the bitcoin wallet wherever the owner may have stored them.
Finally, you might point out that at the moment bitcoin is in its infancy. As a concept it has a HUGE potential, but that the current uses are limited. It is a bit like someone from the late 1970's trying to understand why the TCP/IP internet protocol would be useful to the average person. While the current uses may be limited, the potential is probably larger than the average person can currently even understand. As such, a small investment into this potential while the uses are limited can explode into a significant value in the future when that potential is finally realized. That future could be decades away, but it very will could be 5 to 10 years away as well. It can be difficult to predict just how quickly a disruptive technology will mature.
