Everybody needs a martial weapon proficiency
The shield bash rules say this (emphasis mine):
You can bash an opponent with a light shield or heavy shield, using it
as an off-hand weapon. See Table: Weapons for the damage dealt by a
shield bash. Used this way, a shield is a martial bludgeoning weapon.
For the purpose of penalties on attack rolls, treat a heavy shield as
a one-handed weapon and a light shield as a light weapon. If you use
your shield as a weapon, you lose its AC bonus until your next action
(usually until the next round). An enhancement bonus on a shield does
not improve the effectiveness of a shield bash made with it, but the
shield can be made into a magic weapon in its own right
Shield proficiency says this:
Benefit You can use a shield and take only the standard penalties.
Normal When you are using a shield with which you are not proficient, you take the shield’s armor check penalty on attack rolls
and on all skill checks that involve moving, including Ride checks.
Shield proficiency doesn't give you any kind of weapon proficiency with shields. It gives you the ability to use the shield and not take the armor check penalty. In order to not take a penalty for using a shield bash, you need that martial weapon proficiency. Classes that give you all martial weapons take care of that pretty easily, like a level of Fighter (or Radiant Servant of Pelor if you're a Cleric).
What about "Simple Weapons Only"?
The other classes you mentioned actually have a list of what they're proficient in, the Cleric's "simple weapons only" is just shorthand for a list that has every single simple weapon on it. It doesn't mean that Shield Proficiency works differently for Clerics than it does for everybody else.
It's also worth noting that the Cleric says "all simple weapons", not "only simple weapons". It's not a special rule or exclusion, it's just a shorter way of saying it than listing every simple weapon.
Pathfinder - The Same
From looking around, this appears to be the same in Pathfinder. The shield bash rules are basically the same, the shield proficiency rules are worded a bit differently but don't affect this, and James Jacobs (Creative Director at Paizo) agrees.
In fact, the Paizo FAQ states clearly that shield proficiency != weapon proficiency with shields.
Light shields prevent you from using that hand for spellcasting.
Each entry there tells you what you can do with that hand when a shield is equipped on that arm/hand:
Buckler: Anything, including casting spells (but with some consequences).
Light shield: Hold items.
Heavy shield: Nothing at all.
Light shields let you hold items in that hand that aren't weapons, and that's it. Spellcasting doesn't qualify.
Best Answer
Unfortunately, the rules don’t explicitly define the terms they end up using when it comes to shields, especially when used as weapons. There are a number of ambiguities, in both Pathfinder and the 3.x rules that they derive from, around their use.
The way the rules end up working, shields can have a number of “modifier” terms associated with them. There are types, e.g. buckler/light/heavy/tower, there are materials, e.g. wooden/steel, and there is whether or not the item has spikes, spiked/(not, unmentioned).
But none of this is made explicit in the rules, which means I am basing this purely on my own extrapolation from the rules that do exist and how they seem to interact (or not) with these terms. I feel that this understanding is consistent with how the rules are written, and also matches what appears, at least to me, to be the authors’ intent, but it is impossible to give a hard-and-fast certain answer here.
In any given place within the rules where shields are referred to and certain categories of modifier are not mentioned, they consistently seem to imply that the unmentioned modifiers are not important and any value for them is acceptable.
For example, in the weapon listings, there is no reference given to the material modifier; wooden and steel shields of a given type are the same, and thus no distinction is made between them. On the other hand, distinctions based on type and on whether or not spikes are present are important, so there are separate entries for light and heavy and for spiked or not (total of four entries, one for each combination).
In contrast, for their armor properties, whether or not the shield has spikes makes no difference, but the material is important for determining weight and cost. Thus, there are entries for light and heavy and for wooden and steel, plus bucklers and tower shields which don’t seem to allow alternate materials, so six combinations, but there are not separate entries for spiked versions (though shield spikes are listed under the options section).
So when the bashing property does not specify spiked or unspiked status, it is saying that it doesn’t care about that property. It only cares that the “type” is light or heavy; whether it’s wooden or steel, spiked or unspiked, don’t matter.
Thus a +1 bashing light steel spiked shield made for a Medium creature would deal damage as if made for a Gargantuan creature (and also would have a minimum of a +1 enhancement bonus). This does make for a fairly-high base damage, but considering that shields are not two-handed and cannot have reach, they make fairly mediocre weapons overall. Base damage is a small factor in overall damage.
Also, note that bashing is a shield property, not a weapon property. That means the +1 in the +1 bashing shield is an enhancement bonus to the shield’s AC, not to the shield bash’s attack or damage values. It counts as a +2-equivalent armor for pricing purposes, i.e. 4,000 gp, not the 8,000 gp of a +2-equivalent weapon. Most importantly, you can magically enhance a shield/its spikes as a weapon in addition to its properties as a shield, so you could have a +2 bashing light steel shield that has a +1 flaming light shield bash. It would count as Gargantuan for its base damage, have a +1 enhancement bonus to attack and damage (not +2), and would add +1d6 fire damage to its attacks. When not used as a weapon, it would have a +2 enhancement bonus to its shield bonus, for a total of +3 shield AC.
For simplicity, here is a table of the damage dealt by bashing shields, assuming no enhancement to the shield-as-a-weapon and ignoring other bonuses to damage (Strength, etc.).