Two of the three are fine 'as is", but they may not be correct depending on the tense of the conversation. Looking at each sentence:
B. I was riding in a bus with air conditioning.
This is fine- although there should be a hyphen between "air" and 'conditioning". Although most people and general spelling and written usage does not put one there, it is standard to do so based on the parts-of-speech of both words. The industry trade association for air-conditioning uses a hyphen too.
C. I was riding in an air-conditioned bus.
This is fine as constructed.
A. I was riding in a bus with air conditioner.
As constructed, this sentence is structurally grammatical, but does not make sense. You could change it to one of the following:
*A. I was riding in a bus with [an] air conditioner.*
This reconstructed sentence could mean any of the following:
- you were on a bus and it had an air-conditioning unit installed that cooled the air;
- you were on a bus and it had an air-conditioning unit physically
on the bus (but this says nothing about the temperature of the air
on the bus.
The article I used [an] is only an example. However, if you use another article it may radically change the meaning of the sentence.
In addition to being mindful of verb tense [ride/rode/riding/ridden] and articles [a/an/the], you may also consider the preposition that you use. In general usage, you are more likely to use "on a bus" rather than "in a bus". However there are instances where "in" is more appropriate or when both in and on are both appropriate and interchangeable.