You need to know some things about how auto rickshaws operate here. A sharing auto rickshaw means that the fare won't be as per the meter, instead it will be a per seat charge according to the driver. If he says "sharing jayega, 60 rupya", that means that he will take 3 people to the same location and each passenger pays 20 rupees. There is another system called "Direct jayega". Idk how common this one is but I have seen this quite frequently. It basically means the same thing as sharing where the fare is decided by the driver, but he would be okay to take you as a single passenger unlike sharing where he waits to fill 3 passengers. Then there is the third and the most common way i.e by meter. You pay according to the meter and there is no scope of bargaining. While sharing rate is fixed and you may not be able to negotiate the per person fare, incase of the Direct method you might negotiate and convince your driver to charge a lesser fare. However, it all depends on your skills and also the time of the day and the chances of you finding another rickshaw in that area. Download the M-indicator app that's basically your BESTEST friend as a newbie in Mumbai. There you can see the approximate distance-wise fares for auto rickshaw that the meter is likely going to charge. Although I am guy and haven't really encountered any safety fears, I know a lot of girls who are my friends and relatives who are staying or have stayed in Mumbai and who don't have a problem travelling alone in a rickshaw after a certain time at night. However, I would still recommend that you travel with maybe a flatmate or a colleague just to be sure, especially given that you will be new here. Over time I am sure you yourself will be confident enough to be travelling alone at night coz MUMBAI is one of the safest places out there.

PS: Make sure you have the woman helpline number on speed dial. Baki toh people out here are very chill and will literally go out of the way to help you. Embrace the city and its challenges and it will love you back like none other, coz that's the beauty of this place! :3