Oh wow. Well first, welcome! Ignore all above posts with the words "winstrol", "deca" and "test cyp". We'll save that for a later lesson.
Generally speaking, there is no difference between the way men & women "should" train. The stuff you are doing is the stuff that you find in the circuit training machines at the gym. Not a bad thing, but you are cheating yourself out of some more productive exercises. The best you can do for yourself is develop core strength & really good form on the basics. If you get really basic, squats, deadlifts and bench presses will do great things for you. This gets you into the realm of the free weights - dumbbells & barbells. You don't need to lift heavy, so don't get put off by the vision of becoming a sweaty, musclebound, shemale. Free weights force you to develop excellent form and balance and also give you a range of motion that you won't get with machines.
Your training split is upper body / lower body. This is very similar to what some good beginning training programs like that presented in the "Body for Life" program. (This is a book by Bill Phillips that introduces pretty diet & training regimen for beginners to the fitness lifestyle.)
As far as "what guys do to bulk up" - the training isn't really what determines how "big" you get or whatever other change you want in your body. The diet will determine that. As I said above, you don't necessarily have to lift heavy, but you do need to not cheat yourself by being scared of stackign the weight on. Lift what you can while keeping good form. Keep the reps lower - for example, if I can do an exercise at a particular weight for 12 -15 reps with good form, I'll up the weight by an increment (e.g. 5 lb for arms, 10 lb for back / chest or 25-45 lb for legs) and try to execute at least 8 quality reps. If I can't do that I'll back off on the weight a little and work back up to 12-15 quality reps. The form & intensity will get you some good result.
Cardio-wise, don't be scared to back off a little on that or change it up. I gather you are doing the same low intensity cardio 45 min 5 days / week? You can try doing 1-2 sessions/week of shorter time, interval training - e.g. on a treadmill, sprint for 2 min, walk or jog for 2 min to get your heartrate back down, then sprint for 2, walk for 2, repeat for say 20 min. Do a couple sessions / week of your regular longer, low intensity cardio. Personally I don't do cardio on leg day because I have already beaten my legs to crap with the training and doing cardio will just overtrain them. Also remember that you are doing cardio on the other days as well.
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