And to complete the answer: only the A bluesscale can be used over all the chords. The D and E bluesscale normally don't 'work' over the entire progression, just on their own chord. Sort of in addition to what noticingthemistake is saying though: the best players can start on any note on any chord, no matter how 'wrong', and make it sound good by resolving it to a note that does 'work'.
Once you've got the mixolydian and bluesscales under your fingers (give it time), you'll see that -although very difficult to perform- even from a 'theoretical' point of view this is not as strange as it looks. We've figured out that on A7 you can play both an A-mixolydian scale, which is: A, B, C#, D, E, F#, G, A and an A-bluesscale, which is: A, C, D, D#/Eb, E, G (transpose this to D and E yourself). These scales obviously have different and common notes. Combining the 2 gives you, for example, a 9-note A-scale that runs like this: A, B, C, C#, D, Eb/D#, E, F#, G, A. The only notes, we've only got 12, that haven't been used are A#, F, and G#. These are ' resolvable' though, you can play an A# and a G# and let it resolve down or up to A. You can play an F and resolve it to E, or even take it to A, via F#, G, G#, A, for example. Some jazz-players use other scales that do contain these notes, by the way. So the final conclusion can be: as long as you resolve it, there are no 'wrong' notes on a blues and all this theory is only a tool. So why learn scales in the first place, you could say?
Learning scales is good, beacuse every scale creates its own atmosphere, which is because you're confining yourself to using a specific set of notes. A blues is ideal practical material to start learning this. Learn the mixolydian and blues scales, as well as the arpeggio's of the chords separately, as a very good start. Just remember that you can switch scales even within a bar, and that it is allowed to play notes outside the scale, as long as you resolve them. Scales are a very practical tool to learn how all the different notes in the scale sound against the chord, or better what tension they have towards the chord. Playing the scales, you will hear that some notes create a lot of tension/ dissonance, like the Eb on A7, others will have less (A on A7 as the most obvious example, but also the other chord notes: C#, E, and G). The resolving 'thing' is taking a note with a lot of tension, like the Eb, to a -the easiest is: nearby- note with less tension, like the E.
I'm sure this will give you enough practice material for the coming years, just as I'm still practicing all this.