In some parks, I take my bike into the restroom. If it were crowded, I wouldn't, but so far I haven't had any problems.
When I was building up mileage, I felt more secure when I took plenty of snacks. I think this is more psychological than nutritional, but it works for me.
Good luck -- sounds to me like you can do this. I agree plenty of breaks will help. It really is thrilling to increase your mileage.
Pam



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