Those 3 letters و - ب - ت are called "حروف القسم" (swearing letters), they all can be used to give the same meaning but there are differences between them:
1) ب : can be used with the "swearing verb" "فعل القسم" , and can be used with all nouns and pronouns, examples:
بالله سأسافر = with noun
"ويحلفون بالله إنهم لمنكم" \ "لا أقسم بيوم القيامة" = with verb and noun
يا رب أقسمت بك = with verb and pronoun "ك"
2) و : can be used with all nouns, but NOT pronouns, and can NOT have a verb, examples:
والله سأسافر \ والنجم إذا هوى \ والسماء والطارق
3) ت : can ONLY be used with the name "ALLAH", and can NOT have a verb, example:
"قالوا تالله إنك لفي ضلالك القديم"
Note: because the "ب" is the only form that can have a verb, it's the only form that can be used for requests, as in swearing that someone else should do something, as in "بالله سافر" (by Allah, travel) because it's originally "أقسمت عليك بالله" (I swear by Allah on you "to do this") , and it's shortened to "بالله" or "بالله عليك" , other forms cannot be used in the same manner.