I see there as being 2 basic ways to do it in Shotcut.
Option 1: Add a Motion Tracker filter on the face of the person talking by adding the filter to your video track with the people. Once the filter is added, drag the green tracking box around the talking face and click Analyze to get started. It can take some time for the Motion Track to do its work. Then the resulting data can be used to tie to various filters via keyframes. You can add a Size, Position & Rotate filter to your speech bubble image (perhaps on another video track above your talking people footage), causing its position to follow along with the talking head. You can offset it from the head using a second Size, Position & Rotate filter if one filter doesn’t do the trick.
Option 2: Use Glaxnimate to both draw and animate the speech bubble with a tail that points to the head of the person talking. This is a lot more advanced, but with Glaxnimate you can animate shapes with nodes, colors, lines, text, etc - as in your favorite vector graphics software. I don’t have experience doing this, but I get the impression a lot is possible with Glaxnimate - kinda like Flash animation back in the day or more modern equivalents.
For the speech bubble itself, you could use a transparent PNG for the bubble if you don’t want to try to learn Glaxnimate (do an image search for one or draw it yourself with an image editor), and add a text:simple filter to it to write whatever text you want. You can show and hide the bubbles when each character is talking, or if there aren’t too big of pauses, just leave the bubbles always there and change the text inside them with keyframes.
Sorry, this is quite a generic, broad answer. It would take quite some time to create a step-by-step tutorial, but maybe you can start by looking through the list of filters to imagine different possibilities - Motion Tracker, Text:Simple and more. Or maybe someone else will answer more thoroughly than I did.