Does the Catholic Church teach that we can choose when to use an indulgence? Let's say you've done what is necessary to get an indulgence, but you're pretty clean most of the time and want to use it only after having accumulated a significant amount of venial sins. 

Whether it be asking priests to activate it at a certain point in time or even being given the authority to activate it yourself when you see fit, could you choose when to use an indulgence? 

Maybe you're on some kind of trip and you can't take the Eucharist, but need the spiritual assistance. Of course, extraordinary grace is out of the question; that would be too easy for this scenario.
Can we choose when to use an indulgence?

The short answer is no.

Here is the thing: Indulgences are applied to the soul at the moment that all the requirements of gaining a particular indulgence (partial or plenary)  are accomplished. 


  The Church has always taught that indulgences do not apply to sins not yet committed. The Catholic Encyclopedia notes, "[An indulgence] is not a permission to commit sin, nor a pardon of future sin; neither could be granted by any power." - Myths about Indulgences


What an indulgence is not:


  It is not a permission to commit sin, nor a pardon of future sin; neither could be granted by any power. It is not an exemption from any law or duty, and much less from the obligation consequent on certain kinds of sin, e.g., restitution; on the contrary, it means a more complete payment of the debt which the sinner owes to God. It does not confer immunity from temptation or remove the possibility of subsequent lapses into sin. Least of all is an indulgence the purchase of a pardon which secures the buyer's salvation or releases the soul of another from Purgatory. The absurdity of such notions must be obvious to any one who forms a correct idea of what the Catholic Church really teaches on this subject. - Catholic Encyclopedia


Here are a few points on indulgences from the Vatican:


  To gain indulgences, whether plenary or partial, it is necessary that the faithful be in the state of grace at least at the time the indulgenced work is completed. 
  
  A plenary indulgence can be gained only once a day. In order to obtain it, the faithful must, in addition to being in the state of grace: 
  
  — have the interior disposition of complete detachment from sin, even venial sin;
  
  — have sacramentally confessed their sins;
  
  — receive the Holy Eucharist (it is certainly better to receive it while participating in Holy Mass, but for the indulgence only Holy Communion is required);
  
  — pray for the intentions of the Supreme Pontiff. - THE GIFT OF THE INDULGENCE.


Now if the faithful have the interior disposition of complete detachment from sin there is no reason to save up points for a rainy day since they are in earnest about remaining in the state of grace at all times.