Scales to Play Over A#dim
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A A#dim chord contains the notes A# – C# – E. Any scale that includes every one of those 3 tones fits over it — from the root A#, that means A# Blues, A# Locrian, A# Half Whole Diminished, A# Whole Half Diminished, A# Gypsy Major and A# Gypsy Minor. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
A#dim is also diatonic to one major key: B major (relative minor G#m). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.