I agree that there will likely be some new bureaucracy created by Brexit, but I don't think its impact is likely to be all that significant in the grand scheme of things because:

A) The EU already has tons of bureaucracy. Compared to all of the meetings on migration, the environment, food safety, transport, inter-EU trade partnerships, non-EU trade partnerships, Antici/Mertens meetings etc. etc. the meetings with the UK will unlikely be a significant additional burden on the EU. They may be a more significant burden on the UK, but it's difficult to know for sure.

B) There likely would have been new bureaucracy regardless of how the vote went. Given how close it was, I'm sure that there would have been efforts by Cameron and co. to shift the UK's role within the EU, which would have similarly led to new meetings. The meetings are probably going to be more numerous than they would have been if Remain won, but they might actually be more efficient due to Brexit, since both parties want to limit uncertainty and the fastest way of doing that is to get new agreements signed ASAP.

Your strike analogy implies that all UK-EU trade and production is going to suddenly cease until new agreements are in place. EU-UK trade today is pretty much the same today as it was yesterday. Will EU investment in the UK will decrease until new agreements are in place? Probably. But it's not like factory workers walked out of a job. The workers will keep working, trucks/ships will keep trucking/shipping, and bureaucrats will keep on bureaucratizing. This isn't your employees going on strike. This is your employees deciding they want to switch to a different union in a bargaining year. Sure, you'll have to negotiate a new contract, but you likely would have had to do that anyway.

EDIT: As for comparisons to other countries, they all have bureaucratic trade deals and coalitions, from the TPP and NAFTA to BRICS and the SCO. All of those require a significant amount of bureaucratic upkeep, and each of them was created without setting member states back a decade in terms of trade.