(Why is “bra” singular and “panties” plural?)
As pointed out above, bra is short for brassiere which is a word for a single object, whereas any item of clothing that covers both legs separately is referred to in plural as it comprises two leg coverings put together. Eg. trousers, pants, pantaloons, the full grammar being “a pair of pants”. Underwear is a shortened version of these, therefore is plural, eg. panties, knickers, undies.
Strangely enough you cannot refer to a single trouser or a single pant, it is “trouser-leg” or “pant-leg”!