The WhiteHouse bar near Manish Palace is a good option if you looking for "entry". I have never been there yet, but from FRs posted by a lot of mongers in the past, it sounds like they have good stock. Standard charges inclusive of bar fine and lodge rent is around 4.8k.
Another option for "entry" which is a little more expensive is Nightingale in CBD Belapur. The charges there are either 6.2k or 7.2k depending on the girl. The girl's rate is either 4k or 5k while the bar takes 2.2k (inclusive of lodge rent). I have taken a couple of girls out from here in the past.
There are a lot of cheaper options where "entry" is not really guaranteed - Deepika, Kiran, Amit Palace, Laila and Kishore in Shirvane (most girls do go out for entry) ; Sneha and Sai Darbar in Nerul; Mayur in Sanpada ; Sadguru, Sairat, Baba Palace and Blue Star (got raided a few weeks ago) in Vashi ; Savali, Bela in Mahape ; Rasna, Ramesh, Vikas, Sangeet in Turbhe's Janta Market ; WhatsApp and another bar opposite it in Turbhe Naka ; Baywatch, Akshay Palace, Love and one more (Saigeet?) in Turbhe MIDC... and a lot more in Navi Mumbai. In some bars you have to negotiate directly with the girl and meet them after bar hours.
I am sure there are a lot more bars that don't get mentioned here on this thread. I personally have a list of around 30 that I would eventually like to try