Your bank should also provide this service for free. There is no reason they should try and charge you for this. Years ago I banked with Suntrust and they offered an excellent online banking system, but charged $8 per month to use it. I switched banks to one of their competitors that didn't charge and saved myself $96 per year. Banks have to understand that charging for this type of thing is a sure fire way to shed customers. The service is a convenience for users, so that attracts customers, and because customers can perform transactions without using an ATM, a branch teller or calling someone on the phone, it is saving the bank money. I am surprised that seven percent of the survey respondents said they would be willing to pay a fee for mobile banking. That is about seven percent more than I expected.
Banks go a long way to make sure their services are secure. It is really their money at risk, not yours. You should have a difficult to guess password of course. This can be a pain to set up on a phone that has a T9 input system, but it is worth the effort to have a mix of upper and lower case letters with a few numbers and symbols thrown in for good measure. That applies to all passwords you use, but especially to mobile and online banking.
If you've not tried it yet, go to your desktop and search for "mobile banking bankname" and see if they have it. Being able to check funds, transfer between accounts and even do a few stock/mutual fund trades on your phone is often more convenient than dragging out your laptop. When traveling, I'd never consider using a kiosk or strange computer either. Transmissions with your bank are secure. If your bank cannot establish a secure connection with the browser it won't let you in the site. However, you never know what keyloggers may be installed on a borrowed computer. In those cases, your phone may be the most secure device at your disposal.