Kobac,
Let me jump on the band wagon.
I, like you, are skeptical about giving access directly to my checking account. So I use my credit card for almost all cases where a vendor insists on a card for payment. Though not as long as a lot of posters responding to you, I have use my banks on-line bill pay, free of charge, for about 8 years without any difficulty at all. For bills that are constant every month, I use the recurring payment method and change it once a year if necessary. I've never experienced any late charges except for Discover Card who insisted on posting my payment two days late consistently. I just dropped them completely.
In 2011, I only wrote 7 physical checks. In 2010, 2 and in 2009,4. I really like on-line payments. I'm retired and when I travel, I don't have to worry about bills piling up.
I have only two instances where I allow direct withdrawal from my checking account; one is my mortgage, the other is my credit card (yes, I only have
1). Both of these are with the same bank that I use for all my accounts, check, savings, credit card, mortgage and home equity line of credit. I can easily monitor all activity through their website.
Make sure you'll comfortable with you bank and go for it.