Tell her you want to do this event ... it's almost 800 miles, and you'd be riding with people for some of it.
http://www.rmccrides.com/lastchance.htm
Some questions:
1. Do you go for bicycle rides every day now?
2. Where do you go?
3. Is it always the same route or distance, or do you do a bit of exploring out there?
4. Is your mother OK with you cycling locally?
5. Have you done a weekend camping trip yet where you cycle out to a local campground, stay overnight and cycle back?
6. If not, when is your weekend camping trip planned?
7. Is your mother OK with that weekend camping trip?
If you've answered "Yes" to questions 4 and 7, talk to your mother and tell her something like this:
She is all right with you cycling in YOUR local neighborhood. 400 miles up the road is another mother who is OK with her son/daughter riding in THEIR local neighborhood. How do you think that mother would feel if your mother informed her that her neighborhood wasn't safe for you?
A lot of people feel perfectly comfortable in their own neighborhoods. But everyone's neighborhood is someone else's foreign country or foreign area ...... and everyone's foreign country or foreign area is someone else's neighborhood.