The bomber needs a remote control so that they can detonate the bomb that they strapped to someone else.
In many (most?) cases, the 'suicide bomber' is being coerced into participating, and can't actually be trusted to fully follow through. The real bomber, the person making and orchestrating the bombings, needs the remote control so that they have control over the detonation.
Because the bombs aren't in phone form-factor, they're big vests packed with nails and shit, just set off by phones. People tend to notice when you walk into the middle of a crowd, drop a large bag, then walk away. Now, in situations where they can pull that off, say crowded busses..., I'm sure they employ that tactic.
Also, I imagine there is a heavier emotional impact associated with 'suicide' bombings.
And because the whole point of a suicide bomb is to send yourself to heaven immediately for killing infidels in the name of Allah. Why would you want to carry on living when you could be hanging around in paradise?
They are likely being watched by whoever has the detonator, and (reportedly) the bombers often coerce the bomb carriers into participating by threatening their family.
Alternatively, the thought of directly disobeying authority figures never occurs to them. Remember that most of these 'bombers' are women (in societies where women are oppressed) or children.
Sometimes they are told that they are just transporting and delivering the device to the actual suicide bomber. Then, a spotter sets them up the bomb instead.
