Alot of things depend upon which state you reside and the crime statistics in the area which you ride and your level of comfort

I have had my share of being run off the road, running into a rapist/fire starter while mt bikeing & road bikeing ect.

When I lived in the south west and road on rural roads, my female rideing partner had no qualms over packing heat in her handlebar bag.

I carry mace and a cell phone in my handlebar map bag when riding solo in the metro west Boston area, but the cell phone does not always work. I like to ride with 1 other person, but sometimes it is not possible. Carrying a concealed wepon is not always an option

Some say one needs to have an "presence of confidence" which deters wierds, other say follow your six sense. There is not easy answer to your question, you have to pick the best solution for you.

My 2 cents....