Hi, you should not have any problem using your culture medium, even if is supply with fetal calf. You just need to incubate them for an appropriate time, most of the papers is at least 30 minutes to be sure that the antymicin A goes inside the cell, inhibits complex III and the apoptotic mechanisms are triggered. 

About the BSA is able to restore succinate oxidation that has been inhibited by a high concentration of oxaloacetate (a natural inhibitor of succinate dehydrogenase). This is because BSA is able to remove oxaloacetate from the binding sites and increase the activity of the succinate dehydrogenase (see Panov 2010).

So, I think that you are not going to have any problem if you have fetal calf during your incubation with antimycin A.

AMA blocks e-transfer at the respiratory Complex III therefore both NADH and Succinate oxidation are blocked. Indeed presence of serum attenuate inhibitory effect but not that much. I would say ~20 microM AMA should bring the respiration down in a matter of 10-20 minutes in the presence of serum albumin.

We haven't much experience with the use of AA as a respiration inhibitor in cell culture due to its scarcely reproducible effect on cells growth.

It depends on the incubation time, if it is a culture during days, try to decrease the proportion of fetal bovine serum to 5 or to 2% because there is the possibility that the antimycin remains sequestered in BSA or another protein present in the serum.

Indeed, serum albumin nonspecifically binds a lot of hydrophobic and charged molecules. On the other hand, Ant. A is a highly specific inhibitor/ For this matter, you can use serum albumin and Ant. A simultaneously manipulating with concentrations and time. I used Ant. A for similar purpose as you. in a great access 20-25 microgam per ml.