Meaning
A vulgar, contemptuous dismissal — literally an instruction to come and kiss the speaker's backside, the Jamaican equivalent of 'kiss my ass'. 'Kiss out' means to kiss thoroughly or emphatically, not to miss out on something; naming 'bumbo' (a crude word for the backside) is what turns the line from an odd request into an insult. Used to reject someone completely, often thrown at a person seen as beneath further argument.
Examples
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Yuh nuh like it? Come kiss out mi bumbo den!
You don't like it? Kiss my ass then!
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Him tell mi fi come kiss out him bumbo wen mi challenge him.
He told me to kiss his ass when I challenged him.
Origin
'Kiss' plus the intensifying particle 'out' (see Kiss out) plus 'mi bumbo' ('my backside'). Part of the wider bumbo/bumboclaat family of Jamaican profanity. Minister Marion Hall — the gospel artist formerly known as the dancehall deejay Lady Saw — later reworked this exact insult into 'Come Kiss Out Mi Bible' (see Come Kiss Out Mi Bible), swapping the vulgar object for a sacred one while keeping the line's confrontational shape.
How it’s used
Strongly vulgar. Not for polite company, elders, or anyone you are not prepared to genuinely offend.