First of all I'd like to point out that "take the bus or take the bus" doesn't make sense, since you're presenting the same option twice. Please correct me if I'm wrong, but I think that the sentence is more likely to be "train or bus" or "taxi or bus". I'm going to assume train vs bus in this answer.
Do you want to take the train or would you rather we took the bus?
Do you want to take the train or would you rather take the bus?
The difference between these two sentences is context. The first sentence will only make sense if both the asker and the audience are travelling together. "we take" implies that you are travelling with the person to whom you are speaking.
The second sentence can be used both in the context of travelling together and travelling alone. If you are talking to someone who is about to travel somewhere, you might ask them how they are getting to their destination: "Do you want to take the train or would you rather take the bus?". This would imply that you are somewhat involved in the journey, but not actually travelling due to the "Do you want" part. For example, if you were buying train/bus tickets for someone else to travel, you might ask them "Do you want to take the train or would you rather take the bus?".
In the context of travelling together, you might ask this to your companion so that they will decide what form of transport you both will be taking. In this case, the two sentences have the same meaning.