Can a union force me to recognize it even if I bought only the assets?

Potentially, yes, and this is one of the clearer examples of an asset purchase not giving a buyer the clean break they might expect. Ontario labour relations law's successor-rights protections exist specifically to prevent a buyer from using an asset structure to sidestep an existing union, and whether they apply depends on the substance of the transaction rather than its legal form — if you're continuing substantially the same business with substantially the same operations, a labour relations board can find that you've stepped into the seller's shoes for bargaining purposes, regardless of whether you bought shares or assets.

This is a different test from the Employment Standards Act's continuity-of-employment rule, and passing (or failing) one doesn't automatically determine the other. A business can be structured carefully around ESA continuity and still face a successor-rights finding on the labour relations side, because the two rules serve different purposes and are assessed independently.

If any part of the business you're buying is unionized, get this evaluated specifically and early, since it affects your labour costs and flexibility regardless of how the purchase is structured. A Treadstone business lawyer can help assess this risk before you finalize deal structure.