Buenos Aires does not have a babysitting culture, and thus there are very few companies who offer this service, and it is even rarer is it to find one that has English-speaking baby-sitters.
One company, World Class Nannies, does offer temporary babysitting services as well as nannies and au pairs. Their website is in English, and everyone on their staff speaks English. Babysitters through this company make between AR$20-25 an hour.
Another way to locate English-speaking babysitters is through classified ads on expat sites like BA Expats, or on websites like Craigslist. Many study abroad students who are looking for a little extra money while living in Buenos Aires will post ads for babysitting on these websites.