In my textbook book It states that the て from of a verb can be used to connect two activities together similar to the particle と and how it connects nouns but with verbs.
ex given in textbook: きょうは ろくじに おきて、 べんきょうしました
Today I got up at 6 and studied
I attempted to make a sentence myself but I'm not sure if I'm using it correctly here
My ex. おふろにはいって、 がっこうに いきました
What I was trying to say is "I took a shower and went to school" and while it feels correct, every time I look at it I can't help but imagine myself getting into a bath and riding it to school. Any explanation on why this is or isn't wrong and confirmation on whether or not I really am using て form to connect verbs properly would be appreciated.