My 13-year-old daughter wants to bike to school alone two times a week for band. It's about a 10 minute bike ride with crossing four roads. My husband is scared, but she is very mature and can bike very well. Do you think to let her bike alone with good bike lanes and safe neighborhoods would be save?
There are things to consider. Is this something she would need to do in order to be able to do band? If she can't get herself there, would she then have to give up doing this activity?
What time of day will it be/lighting? The risk of being hit is going to be higher after dark, all things that involve traffic are. Visibility is reduced to about 200 feet for headlights, etc, in town where overhead lighting is placed, you can have issues with shadows, etc.
You also have to always look at why a child wants you not to take them places. I hate to say that, but as an adult who was once myself a child, and a parent to a couple now grown kids (and some little ones), there are times where what looks like a drive for independence can be a bridge to going to a different location than what was asked for. I am not suggesting that your daughter is doing this, merely that it should be something you always keep in mind. Allowing them to start to transport themselves can be incredibly freeing and simultaneously terrifying.
When it boils down, we went with what we both felt solid on. In the end that will be all that matters. If you push to get a yes from your spouse and something isn't great about it, then you also will end up dealing with potential hard feelings there as well.
I also will say it's likely hard for me to be unbiased. I have a friend who reluctantly started to let her son ride his bike 1/8th of a mile to the neighbor's house because of pressure he was "old enough" and all that. The second time he made the ride, he was struck and killed while she stood and watched. She said she thought it would be safer somehow if she stood and watched him and instead she watched him make a mistake. The car made some loud mechanical noise as it approached from behind and it startled him into turning to look. When he did, he turned his bicycle right into the path of the car and was killed. This is not a common thing. I know that. I also know that uncommon or not, there are always going to be hazards to the freedoms we allow our children and we have to as parents sort out what everyone is comfortable with. It was very hard on her marriage because she was angry her husband had called her "over protective" when she said she didn't like him riding on that road to his friend's house and she felt them like she should have trusted her gut and held off longer. It was a very low traffic road and no one would have ever thought this would happen. I certainly did not.