In relation to your question about the Instagram direct blue bubble, I can easily break it down for you here.
Instagram Direct is apart of the Instagram app, that allows users to contact one another privately by means of sending pictures with a text or comment. In order to do so, when uploading a picture, you either select the 'public' option, or you can select the person(s) you wish to make your photo viewable to.
This means that only those person(s) you have selected, and no other followers, can view this picture.
Alternatively, if you are viewing your Instagram feed, there is a small link on the top right of the page, just above your feed, which links you to Instagram direct. You will receive a notification to let you know if/when you have a new message.
When somebody has sent you a picture with a message on Instagram direct, a small blue bubble - as you described - will be visible on the image. This is simply letting you know that you have an unread message. When you open this image, the sender will get a notification to say you have seen it.
If you respond to the sender, and they respond again, you will again see a blue bubble on the same image, meaning you have another unread message. The blue bubble will be visible whenever you have an unread message on Instagram Direct.