Right at the start, I will warn you that having multiple triggers on one table is not a good idea. Try and merge the actions of the two triggers into one if possible. However, if that is not a solution for you, then read on for my version. (I am not certain if it is practically valid, but go ahead and give it a shot anyway)
CREATE TRIGGER triggerB
ON yourtable
FOR UPDATE
AS
BEGIN
ALTER TABLE table_name DISABLE TRIGGER triggerA
--your processing
ALTER TABLE table_name ENABLE TRIGGER triggerA
END
This question deals with disabling then enabling triggers inside a stored procedure. This is an application of the same in a trigger.
Disclaimer: I am counting on this to fail because altering a table while in a trigger defined on that same table seems like an impossible task. But I have no resources at hand to test my wacky theory, so please test it and let me know if I'm thinking too far outside the box.