Forcing me to give Bank Pin to another website

I would like to pay my kulula.com flight ticket with EFT as my business only has a cheque account.

Whe I choose the EFT option it takes me through to a system called SID. SID assures me that I will be interacting with my bank account....but forces me to give my Profile name and Password on the SID webpage adress.

There is no way I will give my bank password to any other person than to use it at my bank account.

When trying to contact Kulula.com to bring my anxiety to their attention all they do not really care they try and assure me this SID website is legit and that it is ok. I have a principle problem with this...the only page my bank told me to use my profile and passwords is on the bank itself. How does anyone know that their details are not being skimmed to be used by someone else.

I am a Kulula.com admirer, but this aspect of their business policy stinks.