Getting burpless cucumbers is all about choosing the right variety. Look online, and read the descriptions and reviews carefully to find a good one. I've grown an old one for years, an heirloom called 'Lemon' and they are wonderful, never bitter and also burpless. Very productive too, but you must pick them often, and before they get too mature or the skin is tough. If you let them get to the stage of looking like lemons, you might have left them too long.
As Daisy said, keeping the roots cool is important in containers. A light color of container, white or pale colors, will reflect heat. I do all my veggie growing in Earth Boxes and they come in white as well as green, and other colors. They also supply reversible soil covers that have white on one side and black on the other. Since I'm in Florida I usually use them with the white side up to keep the soil cool. Down here, the sun is so high in hot weather that the container is actually shaded by it's shape as well as by the plants for most of the day, so I bought the dark green ones and have no problems.
