beside on what you'd mentioned. รถปั่น also referred to the same.

จักรยาน is really more common and mojority of people say จักรยาน such as ฉันอยากขี่จักรยาน = i want to ride a bycicle. as for รถถีบ ,i am thinking the same with khun ekk, it is out of fashion now as well, it is said among elder people i think.

จักรยาน is the most common word for us. You can use รถจักรยาน but for me I think the word "รถ" make me feel like vehicles that have motors and fuel to drive the vehicles such as motorcycles or cars. If I mean bicycle, I will choose จักรยาน to be the first one, the second is รถจักรยาน. For รถถีบ, I think it is used in upcountry, some provinces might use especially in the southern part of Thailand.

จักรยาน and รถจักรยาน are common. We usually use them interchangeable. รถถีบ is less common and it sound like สามล้อถีบ for me.