If you go and buy something in a shop you always receive a plastic bag, (obviously you won't ask for it if you already have brought your own bag) but how can we reuse them?
In this post I'm going to share how I recycle them. There are many ways, but I will show you only two of them.

1. If you have little bins in other rooms, apart from the main dustbin (which in my case is in the kitchen) and you don't have smaller rubbish bags than the 35-50 liter one (CH), why don't you use a plastic bag you received from a shop? You can find them in many sizes and for sure one is as small as your own room bin. The best thing is, that apart from reusing a plastic bag, you don't get the bin dirty, it also protects it from disgusting smells.
2. I like to go in the mountains and as you probably know the weather can change quickly up there and from one moment to the other you are in the middle of a rainstorm. Your clothes in the backpack can quickly get wet and it can be hard to get them dry again. So, when I pack my backpack I always put my clothes into different plastic bags ( even with  a water resistant model of backpack) because apart from preserving them to get wet, it creates order and you don't have a mess.
These are my personal ways to recycle plastic bags, what about yours?

My family reuses plastic bags in two ways. First, I have a large family, which means a lot of groceries, and we end up with bunches of plastic bags. So instead of throwing them away, we reuse them for the little bins around the house, like you stated in your first approach. Moreover, since we have so many bags, we reuse them for packing small items when going to different places. However, I have never thought of reusing plastic bags to prevent water damage or for better organization of the materials in your backpack. Also, there's this bookstore in my town called Barnes & Noble. They have plastic bags and encourage their customers to reuse and recycle them. I believe they give some type of reward if you return the bags to the store.

For as long as I can remember, like your family, my family has always used the small plastic bags we get from stores as garbage bags for the smaller bins in our washrooms and bedrooms. To be honest, we didn't start doing this because we wanted to help reduce climate change, it was merely because my mom didn't want to have to buy multiple sized bags for our bins. My mom likes to save money so she'll find ways to reuse multiple product containers or bags. Using small plastic bags for garbage bins is only a way for her to save money, but if she realized that doing so is actually a benefit to the Earth she'd be proud and encouraged  to find even more ways to reuse them and other products.