Welcome to the forum.
I'm with Merlin on this one. No need to change a BB or cassette every time you get a new chain. I will be putting my second, non-OEM chain on my Colnago next month and it's only a year old, but reaching 6,000 miles. If your crankset it tight and has no play in it, your BB is good to go. I would also recommend getting a chain wear tool, especially if you own more than one bike.