Conventional off-the-shelf bubble bath should not be used in a jetted tub. The jets cause the water to be continuously in motion, and the bubble bath will foam too much and overflow, causing a huge mess.
Dedicated jetted tub foam bath essences can be used as they are low-foaming and lightly fragranced. It's also important to only introduce oil-free or low-oil products to a jetted tub as the oil tends to build up in the pipes and may damage them and be difficult to remove.
Regular monthly cleaning of jetted tubs is necessary to keep them in a hygienic condition. It's best to buy specific jetted tub cleaners as these will clean the pipes and the tub. Alternatively, bleach and low-foaming disinfectant soap powder can be used.