Certainly, the HPS would help. One shop light is definitely not enough to light that whole box for most seedlings. The HPS alone would be adequate. I'm sure sure on the exact light requirements for your bamboo and bonsai seedlings. HPS plus the shop light (use a blue-white tube such as 6500K to supplement the HPS) would be enough light for just about anything.

Watch out for heat buildup in the enclosed box and try to provide some form of ventilation such as a fan to prevent fungal problems.