Bangladesh isn’t particularly progressive but two of their biggest parties have been led by women for decades. They are known as “the Battling Begums”, Begum being an honourific for women. They’ve only had women as their leader since the restoration of democracy in 1991.
The current PM Sheikh Hasina has been either the PM or leader of the opposition every year except for two since 1986, and that’s counting the year whem neither positions existed due to military junta. She’s the daughter of the Father of the Nation which explains her position. She’s been in office consecutively since 2009 and won 86% of the seats in the last election.
Hasina’s chief rival is Khaleda Zia whose husband was President of Bangladesh before being assassinated in a military coup in 1982. When democracy was restored she got into politics and became PM in 1991. She’s been under investigation for corruption charges since 2007 and was sentenced to 17 years in prison in 2018. She’s still the leader of her party and was released to home arrest in March of this year due to “health concerns”.
Neither of these women are very progressive and they are both know to be corrupt, though only the one who’s not currently in office has been convicted. Hasina passed a law the Digital Security Act in 2018 that allowed to her suppress the freedom of speech and arrest journalists. She is known to rig elections in her favour despite already being in the lead.
It’s not uncommon for women who are the wife or daughter of a previous leader to be the leader of a developing country. Lots of Asian countries like Sri Lanka, India, and Pakistan has been led by women who fit that description. Pakistan isn’t what you would call progressive and they had a female Prime Minister, Benazir Bhutto.