Why do green bell peppers become bitter when cooked?
Thousands of different chemicals, previously spatial separated, are mixed together after thermal death of cells, and kept at high temperature to react well. Final taste will depend on original system, but will develop by way unpredictable theoretically from basic principles.
The answer for a particular biological source requires detailed knowledge about particulars of green bell peppers biochemistry, which is rare.
Generally, there are basically few, possibly combined, options:

Bitter tasting compounds - possibly, but not exclusively alkaloids - are already there, but encapsulated in celular structures and released during cooking.
They are actively created by enzymes released after cell deaths ( like $\ce{\mathrm{alliin} -&gt;[\mathrm{alliinase}] \mathrm{allicin}}$ in garlic)
Thermal decomposition of some substances creates such bitter compounds.

Further reading:
bitter-bell-peppers provides rather the opposite opinion:

Why cooked peppers are less bitter
Have you noticed that raw bell peppers taste significantly more bitter when eaten raw (for crudités or in a salad)? That's because most bitter compounds in food break down with heat. The bitterness doesn't go away completely, but it is lessened.

How to Take the Bitterness Out of Bell Peppers:

Select ripe bell peppers. Green bell peppers are harvested before they fully ripen, which causes bitterness. Choose red bell peppers; they are fully mature and slightly sweeter than orange, yellow or green varieties.
Remove the seeds from the cores. The bell pepper seeds are mostly in the cores, and they are naturally bitter. Slice the top of the bell peppers and place them upright. Use a knife to cut out the cores in a circular motion. Cut open the bell peppers and scrape off the remaining seeds.
Peel the skins. Put your bell peppers in a preheated oven until the skins blister. Let them cool for 10 minutes in a paper bag -- the steam will help loosen the skins. Run cold water over the bell peppers and peel off the skins.
Cook the bell peppers. Add soy sauce, salt or other spices to give the bell peppers flavor. The cooking process will eliminate some of the bitterness, and the seasoning will help mask the taste.

chemistry of bell peppers: