You will I am sure be fine to travel to the EU and then come back with the bike, but bear in mind the 0.01% chance that you get pulled up about it - you'd have to pay duty and VAT on it in addition to the EU VAT you paid when purchasing it.
Let's assume I ride it back from Poland. So far as they're concerned, I left the UK with it.
@Dammit started
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You will I am sure be fine to travel to the EU and then come back with the bike, but bear in mind the 0.01% chance that you get pulled up about it - you'd have to pay duty and VAT on it in addition to the EU VAT you paid when purchasing it.