Bacteria became mitochondria? How did cellular metabolism occur before that? And what made them change? And those must have been tiny bacteria... and what evidence proves that mitochondria were once discrete bacteria? Interesting. I've never heard that before.
Yes, the best understanding that we have now says that bacteria became mitochondria (and also chloroplasts, the agents of photosynthesis. Bacteria are capable of amazing things in terms of respiration. There are bacteria that use iron as an electron acceptor; meaning, that instead of "burning" (or oxidizing) carbon compounds, they use the energy in the carbon to "rust" iron. However, the bacteria that we were before we took up mitochondrion were almost certainly anaerobic, meaning that we turned sugar into alcohol or acetate.
The first aerobic bacteria were very probably small. Membranes are required for aerobic respiration. The surface area law (smaller objects have a greater surface area proportional to volume) meant that it was beneficial to these bacteria to be small. However, that meant that they were more likely to be eaten by larger bacteria.
The evidence that mitochondria (and chloroplasts) were once free-living organisms lies in the fact that they still have remnants of genomes. That's right, mitochondria have their own DNA! It's been about a billion years since they were on their own, so much of what their genome was supposed to do has been transferred over to our own genome, but the remnants of their genome are still there.
What is really interesting about mitochondrial genomes is that they have managed to evolve something that no free living organism ever has. Every free living organism on this planet, from bacteria to plants to you, follows the same genetic code. That is not true for mitochondria, since for a billion years, they have not been subject to the same selective pressures. For example, for every free-living organism, the sequence adenosine-uracil-adenosine signifies the amino acid "isoleucine" when making a protein; however, in human mitochondria, the same adenosine-uracil-adenosine sequence signifies "methionine." This is why I love evolutionary theory! It explains so much!