To draw bubble letters, use rounded blocks as a starting point, and cut in the letter shapes. Make sure to achieve a balance between the 'fatness' of the letters and their legibility.
Write the letters you wish to draw in bubble design out as a guide, then draw rounded blocks in the spaces below each letter. Draw a line through the center of these blocks as a guide. Inside the blocks, draw fat, bubbly versions of the letters above. Work in from the edges, using the space cut away from each block to define the letters. A small amount of overlap between letters is acceptable and can create dynamism in the drawing. When content with the design, define the edges of the letters more strongly and erase all other lines.
Shading makes the design appear three dimensional and "bubblier," so pick a direction for the light source and shade accordingly. The darkest shading should be on the parts of the design furthest from the light. Add layers of shading gradually so as not to overdo it. For added effect, include highlights on areas where the light source would shine directly in the form of an unfilled or light colored bubble.