No Work contract. How to deposit money for Bill pay?

Just go into any bank, hand over the amount in cash, the landlord's account information, and your passport, then ask the bank to send it.  The bank will charge you a small fee and your landlord will receive the money in an hour or so.

I did that several times last year.

You can also do the same thing using Vinaphone or Viettel money transfer service.

I use a online international money transfer. This save heaps in bank fees and rates. You will need the SWIFT bank code which the bank should be able to provide you or you can find online.

For others that may be interested: HSBC would not open an account because I did not have a job at home or own a property here. VietinBank opened one no problem with a Visa debit card attached. You just need your passport, visa and proof of address (3+ months). I used my signed lease agreement (a chopped document was not required). It took a week for the card and a few more goes to get it all set up but it is relatively painless. They have English speaking tellers and an English help line. Make sure that you ask for an online (iPay) login and authorise the card for internet purchases.