I prefer frog tape to the regular blue painter's tape. You can get it at Sherwin Williams, it's pretty expensive, about $7 a roll here, but I think it is completely worth the money. If you clean the glass with rubbing alcohol before applying the tape and press down the edges really well with something like a burnisher or plastic bone folder you will get a much cleaner edge. From your photos, the lines look really nice and crisp, maybe you are just being too critical of your work
And of course I must comment on the freakin' adorable gift bag! So lovely!