ちょっと: Many people know ちょっと means “a little bit” such as 日本語がちょっと話せる meaning “I can speak a little Japanese“. But this ちょっと is used to express the speaker does something casually without much thought or doesn’t want to bother explaining something. There is no direct English translation for that but maybe you can express it with “just”.
タバコ means “cigarette”. The particle を is used to indicate the direct object of the following verb. 吸い is a stem of the masu-form, 吸います usually used with タバコ to mean “to smoke”.
たくなった is the past tense of たくなる. たく comes from たい meaning ”to want to do something” and なる means “to become” or “to reach a certain state”. It follows a stem of a verb masu-form and it means “to become or to start wanting to do something“. So Bunta let go of the steering wheel because he just started wanting to smoke.