Amy, maybe this will help a little.
When first diagnosed in late fall 2009, my blood counts dropped immediately with hydroxyurea, then more with Gleevec. This November (2011), my WBC finally fell into the lowest-normal range (4.0 for my lab). When my WBC were very low, I was given Neupogen, then Neulasta (shots) to increase WBC production (namely neutrophils, white blood cells that fight bacteria). If your counts get too low for his/her comfort, your onc may want you to get these shots. At one time, I gave myself shots at home every other day (if you have young children, they will get bored of this real fast). But you DON'T have to do this! I just didn't have anyone to watch the kids while I ran to the onc. The shots brought me a little over the 1.0 range for my total WBC, (as you know, there are different kinds of white blood cells). And my neutrophils stayed around .9 and sometimes a bit higher. Presently, I stay around 1.0 for my neutrophils, (ANC), without shots. For some healthy people, 1.0 is normal. And I don't know what my average was before CML, so it may have always been around 1.0. My PLT (platelets) still remain low (20-30,000). Some oncs may consider this "dangerous", but I have shown no signs of bleeding and appear to clot normally. I never bruised abnormally with CML, and I still don't. But there are shots and platelet transfusions for that if your PLT get too low. Your hemoglobin (HGB) may also become lower. Most people on this board seem to go just a little below normal. If you menstruate, you may have issues with anemia on a TKI, especially if you begin to bleed heavily. This could turn into hemorrhaging (been there and cured of that with birth control pills). But there are shots for low hemoglobin too. They seem to have a shot for everything.
All in all, everyone has their personal threshold (for everything; blood counts included). Normal for other people may not be your normal. However, it takes time and communication with your onc to find this out. For example, my threshold for hemoglobin was below 6. Most people are transfused at 8.7 or somewhere around. But I was fine at 6. My ANC, (absolute neutrophil count), stays around .9 or 1.0 without shots. So far, I have been OK, (but afraid of jinxing myself if I admit that, so, "poo poo", "kenahora" and the like).
So, if you counts are very low, keep hand sanitizer near and keep your hands away from your face (good advice for anyone, really). My first onc scared the crap outta me and I stayed home for the holidays. It turns out I didn't have to. When I was really low, I did what I had to do AND did what I enjoyed (even went to a public pool with my toddlers---some may consider this ultra stupid, but I guess I was lucky?). Anyway, you gotta live your life (as my onc and members on this board have said to me). I have two little children and one is in preschool, so there is no great escape from the evil germs a-lurking.
Don't think I am recommending throwing caution to the wind and hanging out with a bunch of actively sick people, and "licking the souls of your children's shoes" (borrowed this expression from Trey way back when). My friend's friend's husband (how is that for confusing), contacted a horrible illness, (not sure if it was bacterial or viral), and was in ICU for months, had his organs shut down, damage to his heart, and needed home healthcare. It was touch and go for almost half a year. I think he is OK now, but he was an otherwise extremely healthy young guy that just came into contact with something nasty. Life is a crap shoot. There are tons of things out there that can do a person in. Having CML and low counts magnifies the fear of just about everything bad. If you are like most people, aside from the CML and TKI side-effects, you will likely be in no more danger than most people. But, as a long-time germaphobe and fellow and former very low WBC producer, I still recommend keeping the hand sanitizer in your bag.
P.S. I am doing well and feel great. I am on Sprycel now, but the change had little to do with my CBC. It had more to do with my seemingly flat resonse to Gleevec.