I also recommend Downie's book, which thoughtfully adapts some of the Roman recipes for the American cook. I don't have Jo Bettoja's book, but I have an earlier book by her "Italian Cooking in the Grand Tradition" originally published in 1982 - the year I returned from my first 2-year stint in Rome. It has many of the classic Roman dishes and I've cooked and re-cooked my way through many of them. If you were ever to come across it, get it! Another monograph "The Food of Rome and Lazio" by Oretta Zanini de Vita is terrific for the history of Roman food. It is published by the Regional Tourist Board of Lazio and I couldn't find it on Amazon. If you knew someone going to Rome, you might ask them to look for it for you.
I own both Jo Bettoja's "In a Roman Kitchen" (recommended above) and also David Downie's "Cooking the Roman Way" (link below) and when I went to Amazon to find the Downie link to send to you, was amused to see a review comparing both books - both of which have fine virtues - much the way I would. Were I to make a choice, Downie's "Cooking the Roman Way" would come first. And if you check this link, you will see you can have a used copy for under $4 (versus list price of $25), so perhaps you will buy both.
I'm of Italian heritage and have spent a good deal of time in Rome over thirty years, several times renting a flat for myself and my family so I could market and cook, as well as feast on all the infinite rest that Rome offers, culturally, socially, as well as gastronomically. All to say, I don't buy Italian cookbooks for exact recipes as much as to read them and expand what I've learned through experience and inherited - and think Downie's book a great start because he not only offers a great range of home and restaurant cooking, he gives fascinating and useful background information about methods, and even the history and social mores of certain practises and ingredients.(great sections on making Roman style pizza...preparing artichokes...desalting anchovies...seeding tomatoes...making pasta, ecc. simply explained besides inspiring, emboldening...)
And if you're at all homesick for Rome, his great photos of some of the restaurants and markets and purveyors will be a delight - most likely you'll recognise some spots, maybe even faces. We did. (a few other recommendations follow this link)
Cooking the Roman Way: Authentic Recipes from the Home Cooks and Trattorias of Rome (Hardcover)
by David Downie
Another great book that includes a section on Roman cooking is the classic by Ada Boni, who was the grand nonna - grande dame - of Italian cooking,one of the greats - "Regional Italian Cooking" - This is authentic Italian cooking, plain and perfect. And you can find it used (it is out of print) on Amazon for around $9.
And if you want to learn how to make Italian bread, Carol Field's "The Italian Baker" is it. http://www.amazon.com/Italian-Baker-Carol-Field/dp/0061812668/ref=pd_sim_b_5/104-8751705-3070334?ie=UTF8 She is brilliant, and a beautiful writer, and after years of trying to bake a decent loaf of bread, of any nationality,and dozens of bread books, sh let me succeed. The background history, as well as methods and recipes for breads and baked sweets, make the book a treasure.
Ada Boni's book: