That's why you always put up the influence trade before asking for something - the game runs every integer trade value through whatever algorythm is used to determine whether AI will accept the trade. Late in a game, this means it has to test hundreds of millions of integers until it decides no, there is no value the AI will accept in trade.
Trading for bcs generally doesn't do this, as there are far fewer integers to test, and each unit has far more value. That means the AI is more likely to accept the trade at a lower numerical value, and even if it doesn't accept it doesn't take several minutes to determine that it won't.
As for actually trading influence points, the AI values them inversely (but not at a linear rate) to how many you are offering. offering 100 at at time will get you a better exchange for bc than will offering 1000 at a time. offering more than 1000 is pretty counterproductive, as the trade value drops to nearly zero. Offering 1000 (or more commonly 999) at a time seems to be the best tradeoff between wrist fatigue and trade value 