This has nothing to do with any "written report". While both verbs involve being immersed in water, the *meanings* are entirely different. We cannot tell you which verb to use without knowing the context. You can check the dictionary of your choice. It will take you two seconds.

People do / did sometimes use “bathe” to mean “go to the swimming pool” but it sounds a bit old fashioned, and has the sense of gentle relaxation rather than exercise.

They are 2 very different activities. To bathe is to clean yourself, usually in a shower or a bath tub. Это 2 очень разных вида деятельности. Купаться - значит мыться, обычно в душе или ванне. To swim is to play in a pool or a lake or a river or the ocean. (Or to participate in the sport of swimming) Плавать - значит играть в бассейне, озере, реке или океане. (Или участвовать в плавании) Good luck! Удачи!

I would say swimming is more active. Some people here need to take a look at themselves.

Bathe and swim are not synonyms. Bath means to clean oneself, while swim or swimming is the means to traverse in water.