My advice is stay in Singapore, if you want to work in Singapore.

To me, it's definitely not worth spending 4-5 hours a day commuting to & fro, just to save a few hundred dollars. Like pubee said, if that small sum makes such a difference to your financial situation, then perhaps it's not worth it to work in Sg.

If your new job pays OT, you could use the few hours a day you save (if you stay in Sg) to work extra and get more money. Or you can spend that time learning a new skill or furthering your studies. Or just spend it destressing.

Nothing is more wasteful than time spent commuting.

Which part of Sg will the new job be? If it's on the edge of the island somewhere eg. Changi, Jurong, Tuas, Woodlands, Boon Lay, Punggol etc... then staying at these non-central areas is significantly cheaper. Even if your office is at Orchard or the CBD, you can save money by staying farther away. Just spend a little more time on the MRT, but it'll be nowhere as much as going through the causeway.

You can rent a room in a HDB flat from $100-900. Varies greatly depending on location, proximity to MRT, amenities, aircond, attached toilet and class of flat (executive hdb, larger flats, smaller flats, neighbours etc. foreign workers, locals or expats, blue or white collar etc).

And if you can find someone to share a room, your rental is halved.