From your question I understand that you would like to create geobubble, push button and line plot on a single figure. You can achiveve that with the 'parent' property of all the three components.
For example, the below code creates geobubble and push button on a single figure
f = uifigure;
tsunamis = readtable('tsunamis.xlsx');
tsunamis.Cause = categorical(tsunamis.Cause);
g = geobubble(f,tsunamis,'Latitude','Longitude', ...
p = uibutton(f);
Using this 'parent' property as per your requirement might help you.
Hope this helps!