Try DBS/POSB. Or you can try with Maybank Singapore. Many Malaysians who do not study or work there have an account with them.

I recently open bank with DBS/POSB. Took me less than 10 minutes. I don't even stay / work there. My main purpose is for online transactions only because I do not trust Maybank (yet) ^^;

I tried another bank, they say I have to work/resides in Singapore to be eligible. The bank is red in color, can't remember much.

DBS also do not charge any fee when we use their Singapore issued ATM/VISA debit card to withdraw money through their ATM in DBS Hong Kong, DBS Taiwan and DBS Indonesia.

Recommend DBS bank for Malaysian to open bank account in Singapore. Easy to open, excellent service (much better than Malaysian banks  ), just 10-15 minutes, they even fill in the bank opening form for you. Also instantly eligible for ATM/debit card, internet banking and secure device.

My main purpose is for easy credit to my singapore investment, diversify my cash and asset holdings, safeguard my money against sudden devaluation and also just in case this country tells me ' you tak suka, you keluar!'.