Colour of the bead in borax bead test is mainly due to the formation of

Borax on strong heating loses its water of crystallization and then shrinks forming a transparent glassy bead of sodium metaborate (NaBO₂​) and boric anhydride (B_2​O₃​) as shown in reaction given below:
Na₂​B₄​O₇​.10H_2​O→Na₂​B₄​O₇​+10H₂​O
Na₂​B₄​O₇​→2NaBO₂​+B_2​O₃​
Boric anhydride, being non-volatile displaces more volatile acidic oxides and combine with basic oxides present to form metaborates which are identified through their characteristic colours.