Sounds like there's other issues that might need discussed? When he was gifted to you, was it discussed between previous owner and you two leasers whether or not the other girl's lease would be continued after you took ownership? Do you want her leasing your horse?
That aside, if you don't want to share, buy a second bridle and a leverage bit. One of your bridles will then have a snaffle, the other a leverage, and no need to switch out bits. Of course, then you might also want to have two sets of reins. I noticed that you are in Argentina, so might not have as many options as I personally am used to, but surely there are cheap bridles or second hand bridles that you could buy?
OR, if you were to change your mind about sharing, you could put a leverage bit on your bridle and a snaffle on hers, so that your bridle would be the one being used less often. And you can always clean your own tack. I do mine, I wouldn't really think of asking someone else because I can be very particular and don't have confidence they can do it to my standards. My philosophy "if you want something done right, do it yourself!"
"You can do something wrong for thirty years and call yourself experienced, you can do something right for a week and experience more than someone who spent thirty years doing the wrong thing." ~WhattaTroublemaker