It works, with or without my .
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AnonymousIs this how you naturally use 'come to mind'?It didn't come to [my] mind to ask her if I could pay for half.It seems to me that 'my' ('your', etc.) is not often used in that expression, but it fits pretty well in that sentence.
AnonymousIt didn't come to [my] mind to ask her if I could pay for half.Somehow, it seems 'off'—either we don't use it in that position or something, or it's a different idiom needed? I cannot see the problem, but I keep wanting to change it to these:
AnonymousIt didn't come into my mind to ask her if I could pay for half.First choice.