Mryntu

Imagine a planet of roughly the same size as Earth with the same amount of land, the same atmosphere and the same proportion of water (other planetary parameters may vary from Earth like) that has suddenly become gravitational locked so that one side always faces the sun.

Is there any scenario in which after a sufficiently long time large tracts of the ocean bed on the side facing the sun would be exposed to the atmosphere and all of the planets water would end up locked up in ice on the dark side? If so what special conditions would allow it and if not what processes would prevent this from happening?

Researchers have modeled this very question

See their Figure 1:

Apparently there are 3 relevant variables: less water, less geothermal heat flux, and more night-side continental area will increase the effect. Geothermal heat flux is how fast heat from the planet's core reaches the surface.

According to them, if earth became tidally locked, roughly half of the oceans would freeze. If you want to increase the effect with the same amount of water, simply change the other two variables: continents are more concentrated and end up on the night side, and they don't get much heat from the core.

And Now the Part Where I Ruin Your Day

However if the tidal locking is natural, this scenario has big problems. In order to move the habitable zone close enough to the star for tidal locking, it has to be a small red dwarf star. While long lived, young red dwarfs throw lots of huge magnetic and radiation flare tantrums. For a planet's atmosphere to not get blasted off during puberty, it has to have a very strong magnetic field -- think a fast or a huge electric generator. But unfortunately, tidally locked planets spin very slowly. That means you need a larger super-earth type planet to generate that field. You might be able to roll with that, but the kicker is that your powerful magnetic generator also makes a ton more geothermal heat to melt your ice. Maybe the planet's core is lined with space shuttle thermal tiles?

But Wait, It Gets Worse

A comment on another answer indicated a bigger question, about the ice cap swinging toward the sun. Unfortunately that's a no-go. Apart from the fact that surface water is only about 0.02% of the earth's mass, tidal forces relative to the center of the earth are actually away as well as toward:

In the left picture, imagine subtracting the center average arrow from the outside arrows to get the effect from earth's perspective. It's not quite as much on the backside, but the icecap still won't be interested in wandering past those side parts. Sorry pal.

Yes -- this scenario is definitely possible. Climate models for tidally-locked planets find that for planets with relatively thin atmospheres with modest amounts of water, it can indeed all be trapped on the dark side of the planet as ice (technical references here and here).

With a bit more water or a bit thicker atmosphere you can have an Eyeball planet with enough water that the zone of permanent sunset/sunrise (what I called the "ring of life") can be quite pleasant. See here for an explanation of that type of hot Eyeball planet. There also exist cold Eyeball planets with lots of water (see here). A good candidate for an Eyeball planet is Proxima b.