This is not about nuances as much as it is about grammar. Particles mark values for certain slots, in this case mostly the が slot (the subject, who does the fighting) and and the と slot (the opponent of the fighting). These slots are associated with the main verb 戦う, and different verbs expect different slots with different levels of requirement (but the が slot is often highly required)*.
Xは often brings X to the が slot. Xで doesn't bring X into any of the required が and と slots, making the sentence incomplete (not in the sense that it's ungrammatical, but it requires the context to provide the missing values).
ボブたちで戦ってる
This makes the subject (or the が slot) and the opponent (or the と slot) implicit, and has extra vagueness. The implicit subject could exactly match ボブたち, but it could be something else. There might be a larger group that is the subject of 戦う, and ボブたち might be select representatives - in that case it's reasonable to assume they are fighting together, not against each other. There might be controllers that is the subject of 戦う and ボブたち might be merely tools/puppets - in that case, they might be fighting together (under the same controller), and they might be fighting against each other (under different controllers on each side).
I'm not saying you can draw these interpretations from one particle alone, though. They will simply be possible with that sentence, while in the other sentences they will probably be incompatible with the explicit subjects (except for in some very contrived context).
ボブと戦ってる
This is kind of similar in being vague about the subject, but it at least fills the と slot.
*: This concept is called 必須格 in Japanese linguistics. I don't know what is the correct term in English - "required case value"?
How to disambiguate と
-と can be used to mean 'together with _', which is optional in a lot of verbs, in addition to the opponent slot mentioned above, leading to two possible interpretations. The required slot (the "opponent" interpretation here) usually takes precedence over the "together" interpretation, because it needs to be filled somehow, but not always. When the context heavily implies the existence of someone else on the same side to the subject, that interpretation could be preferred.