Well, quite honestly, none of you were right in your reasoning. The ultimate answer, though, is that Bloodrider cannot be used to cancel Catelyn Stark.
Bloodrider cancels character abilities. Character abilities are effects on character cards that are triggered when the card is in play. Since Catelyn's effect is triggered while she is in a player's hand, she counts as a character effect, not a character ability. Bloodrider can no more cancel the effect on a character card that is triggered while that card is in a player's hand than it can cancel an event card.
So you were in correct in that Catelyn's effect does not meet Bloodrider's play restrictions and you could not use it in the first place. (Interestingly enough, this is the same reason Bloodrider #2 cannot cancel Bloodrider #1.) However, your opponents were wrong in that Catelyn is not "already in play" when you would cancel her effect because a cancel would interrupt and stop the resolution of her effect - which is what puts her into play. Their general idea that "you can't cancel something that is already resolved" is true, but at the same time, you cannot resolve something before there is an opportunity to cancel it. Bloodrider isn't a legal cancel for Catelyn, but if you had something that said "cancel a triggered effect," it could absolutely be used against Catelyn, stop her effect from resolving to put her into play, and leave her in your opponent's hand.
Of course, the fact that the cancel would leave her in your opponent's hand should tip you off that it is almost entirely pointless to cancel her effect because her owner could just trigger her effect all over again.
1) Action is initiated
After a player initiates an action, the timing
For the initiation stage of any player action, a
player must go through the following substeps,
in order. The first step is always revealing the
card or declaring the intent to use an ability.
a) Determine the cost (to either marshal the
card or pay for the card's effect) or costs (if
A Game of Thrones LCG Timing Structure and Flowcharts
multiple costs are necessary for the intended
b) Check play restrictions, including
verification of applicable targets.
c) Apply any penalties to the cost(s). (Any
effects that modify a penalty are applied to that
penalty before it becomes a part of the cost.)
d) Apply any other active modifiers (including
reducers) to the cost(s).
e) Pay the cost(s).
f) Marshal the card, or trigger the effect.
Choose targets (if applicable) and proceed to
2) Save/cancel responses
e) and f) that you pay before you trigger. So when triggering bloodrider, he's already in play(as a cost), so his ability should be considered as a character ability, which can be canceled by The Iron Throne or another Bloodrider.