Once you've got more than about 50 people below you, you should be able to get a trip line. Whether or not it's the one you really want, however.....
As a very junior trip line holder, you may actually be better off going for a blindline rather than a tripline with potentially no days off that you want (the trips you will get won't be much different). You're then CAP protected and are generally likely to work a little less hard than a Tripline holder.