I used to work as a bank teller and I think electronic banking is great. My only suggestion, aside from making sure to deduct it from your checkbook, is to also check to make sure it was deducted properly on your statement. There were a few times where the BANK mistakenly would deduct the same item twice, and this would happen to all billpayers. It wasn't a regular occurence, but it happened at least 3 times during my 5 1/2 years there. While the problem was rectified within a couple of days and for most people it wasn't an issue, it did affect a few.
Also, check to see if your bank charges for that service. Sometimes banks do charge a monthly fee for the service, but if you set it up with the company you're paying, it's free. For example, our local telephone company deducts from checking with no charge. It is probably easier to set it up thru the individual companies because they will deduct from your account the exact amount you owe. However, if you do that, chances are you won't be able to specify the date you want it paid. With the bank, you might be able to specify the date, but you might have to do something like call in to an automated service on the date you want it paid to pay a specific amount, unless it's something where you know the amout is going to be the same every month.
Hope I didn't just make this more confusing! There are lots of options, you just have to decide what works best for your needs and your bookkeeping system.