If I have a chord progression which is basically 1, 5, 4, 1. Example F C Bb F.
What is the diatonic or consonant pentatonic scales to play over that and why?
The answer to this question requires a statement that "best" is subjective and you should play whatever scales you think sound good, whether they're consonant to the chord progression or not. That being said, if by "best" you mean the most consonant or the most traditional, the answer would be one of the following:
First, the obvious answer is the major pentatonic scale of the tonic note (in your case F). This can sound a little bit bland because it is only composed of five notes (of course you could always add embellishments if it seems aesthetically pleasing). The advantage with this is that the notes will always be harmonically valid and consonant. The disadvantage would be that it is much harder to create tension, especially with a 1 5 4 1 progression. However, again depending on the style of music you are playing, this choice could help you achieve a sense of minimalism if that is a desired sound.
The second answer is to play in the tonic of what chord is currently being played. This will result in you playing the notes of F major pentatonic then C major pentatonic then B flat major pentatonic then back to F.
Really, there are two ways to approach the second suggestion. The first is to strictly play the major pentatonic of tonic to whatever backing chord is happening. The second is to actually modulate around F! Switching from F major to C major would be the first way, modulating from F major to F lydian would be the second. In F lydian you are still playing F as a tonic, not C, so in reality this distinction between these two approaches will be found in how you play the root in your phrasing. If you choose to resolve root notes of the F tonic for each chord then you are modulating to modes of F. If you are resolving the roots of each of the chords then you are playing in C major and B flat major. You could always switch between these two ideas during the song if you feel one of them is too stale.