Is there a Bedside mode capability for iphone?

I don't think there is, but some apps do have a silent mode that allows you to restrict notifications between any given two times of the day. You could also turn off notifications before you go to bed or put the phone in silent mode, but it's not quite the same, I'm afraid.

Alternatively, turn on Airplane Mode, it won't affect your alarms, but it will stop any internet-triggered notifications

I am migrating from BlackBerry to iPhone and can't figure out how to turn off all notifications and sounds other than the phone ringing and the alarm clock so I don't have this thing buzzing, lighting up, vibrating and whatever it likes to do at night.

http://manuals.info.apple.com/en_US/iphone_user_guide.pdf

Do you see that feature in the User Guide? If not, it doesn't exist. No secret functions.

There is no quick and easy way to silence all alerts in iOS while allowing the phone to ring. The alarm will always sound, even if the silent switch is activated (provided the phone is not powered off entirely).

Many people have asked for a 'bedside mode' similar to that offered by other smartphones. In this state, the alarm would still sound if set, and the phone would ring for incoming calls, but no other alerts will sound.

Though it can't be done in software settings, the equivalent can easily be acheived by plugging your headphones into the phone. The alarm and ringer will still sound through the phone speaker, but all other alerts will play only through the headphones.