Blow bubbles through the straw by puffing the cheeks then forcing air through straw. You will not be using your lungs at all!
Now try blowing bubbles with normal air while gradually allowing some air to puff into the cheeks. When your cheeks are fully puffed, stop blowing bubbles. Then, blow bubbles with cheek air as in step 3. Repeat this process several times.
Repeat step 4, but without stopping between blowing normal air and cheek air.
Blow bubbles with cheek air as in step 3, but breathe in through your nose at the same time. Practice motion without straw and water, first, to keep from inhaling water on the first try! Repeat this motion several times, until it begins to feel more comfortable.
Repeat step 4, this time breathing in as you force the air out of your cheeks.
Repeat step 4 again, breathing in as you force the air out of your cheeks but without pausing between the normal and cheek air. Try to keep the bubbles continuous. This is the key step: repeat this as long as needed to become comfortable in keeping the bubbles coming. Go back through the previous steps as needed.