There seems to be a very wide variation in how people pronounce the "r" in Esperanto - sometimes you can (roughly) identify the nationality of someone with otherwise very neutral pronunciation just based on the "r" (try listening to Pola Retradio or Radio Vatican in Esperanto) -- uvular r, tapped r, trilled r, etc.

Frankly, I wouldn't worry too much about it. For an American (?) pronouncing the sentance "mi fartas bone", I would be more concerned with making pure vowels than the "r".

If it helps you feel better, here is an .mp3 file of me reading the first Ekzerco in the Fundamenta Krestomatio -- plenty of "r"s. Should be good for a laugh

Amike,

Paul