I agree with Baystateblue and Denis: version A sounds more "native". Version B is clear and understandable, but I haven't heard it from native speakers. Honestly, it sounds as if version B is too much effort (says he from the land of lazy Rs). The English Rs are "liquid" - almost between a vowel and a consonant. With the exception of a few rolled R variations, most English pronunciations of R can also be continuant. There are a few pronunciation videos for R online. However, the ones I've found are all American versions (there are at least three variations). That is to say, I pronounce my Australian R differently. In practice, you only really need one style of using R that works, so don't try to learn them all. Extra note: pay attention to the way you pronounce "L". It needs to be thicker and warmer. It is a continuant: LLLLL...

melaminefree, I agree with Babystateblue. In version A, you are using the American initial position R. Version B is an approximation of the American R that is sometimes called the International R. You make this approximate sound if you don't raise the back of the tongue up far enough towards the roof of the mouth. In the American R the back of the tongue is bunched high so the sides of the tongue touch the back side teeth, which produces a different timbre. The received English R is a different story. It is made more forward in the mouth but sounds much like the American R to the ear.

I think it is very hard for anyone but an expert in English phonetics to say for certain that a given sound does not occur in any dialect of English, simply because there are so many. But I can safely say that I've never heard a native English speaker use version B. However, the difference is quite subtle and if you did decide to use version B, I don't think people would have difficulty understanding you.