Step 1 :First, we need to generate all possible permutations of the four singers Enrique, Katy, Rihanna, and Bruno. These permutations are represented as strings of letters such as ERBK or KERB.
Step 2 :The total permutations are: 'EKRB', 'EKBR', 'ERKB', 'ERBK', 'EBKR', 'EBRK', 'KERB', 'KEBR', 'KREB', 'KRBE', 'KBER', 'KBRE', 'REKB', 'REBK', 'RKEB', 'RKBE', 'RBEK', 'RBKE', 'BEKR', 'BERK', 'BKER', 'BKRE', 'BREK', 'BRKE'.
Step 3 :Next, we need to filter out the permutations where Katy (K) and Bruno (B) perform consecutively.
Step 4 :The permutations where Katy and Bruno perform consecutively are: 'EKBR', 'ERKB', 'ERBK', 'EBKR', 'KBER', 'KBRE', 'REKB', 'REBK', 'RKBE', 'RBKE', 'BKER', 'BKRE'.
Step 5 :Finally, we express the event 'Katy and Bruno perform consecutively' as a set.
Step 6 :The event 'Katy and Bruno perform consecutively' can be expressed as the set \(\boxed{\{'EKBR', 'ERKB', 'ERBK', 'EBKR', 'KBER', 'KBRE', 'REKB', 'REBK', 'RKBE', 'RBKE', 'BKER', 'BKRE'\}}\).