Is it easier to bankrupt yourself in BtS than in vanilla?
Apparently, yes. I never played anything but BtS but I looked around for you a little bit
https://forums.civfanatics.com/threads/civic-upkeep-explained.148840/page-2
I didn't dig too much but various times it's been pointed out that updates to civic cost calculations have made them more expensive with successive patches, namely 1.52 and 1.61, and again in BtS at some point. The city maintenance formula was also updated a few times and they removed the lesser cost on the Slavery civic at some point.
But yeah, basic rule of thumb what AcaMetis says. Try not to tank your economy too hard before Currency, or at least Alpha (so you can build Research to get to Currency). It's the major economic bottleneck tech. The easiest way to do so is expanding less and skimping on units, so practice your diplomacy.
There are other little tricks to keep pushing the economy even when it seems cottages aren't doing it:
-wonder failgold, as suggested already. Stonehenge is best since it's easiest to access and the AI builds it early, Great Wall/Mids or Temple of Artemis/Oracle can work too
-get to writing and whip Libraries in any city with +4 food surplus. Run 2 scientists to keep crawling forward in tech
-cottage over calendar resources and things like riverside wine for more immediate commerce yield; only replace them later. Bananas and Sugar can serve as almost floodplains for cottages/farms.
-make sure to keep The Wheel and Pottery high in your tech priority; hooking up cities reduces their impact a tiny bit and cottaging is obvious
-Make connections to the AIs early. Either road to them or get Sailing. You'll notice how much the trade routes help out the more dire your economic situation is.
-NEVER fully tank the economy unless you have at least Pottery or Fishing! Working coast can save you from stagnating sometimes before getting Pottery.