the reality is that there aren't enough beds in psychiatric hospitals (or on private units) for people who are permanently severely disabled and unable to function at all because of their psychiatric issues much less for every one of us who thinks, "life would be easier if I ate kitty litter until I popped" (trying to be humorous, no plan/intent to eat kitty litter until I pop)
I'd say the most important thing you can do when discussing suicidal thoughts is to be transparent...
be real about the frequency, intensity, duration, etc (happening every minute/hour/month, reactive thought or so strong you had a knife in your hand, fleeting thought or something you can barely shake)
don't fear the hospital, it's not there to hurt if your professionals think you should go... you probably should go... a lot of clients I know see it as a vacation b/c it's a time where they can focus on their lives as individuals without responsibilities of the outside world (that being said, I advocate learning to solve crises in real world situations as the most successful treatment whenever possible)
I have heard everyone has those thoughts at some point, I've had them... most people I know have had them... one of my MOST STABLE friends (she's been a therapist for 7 years) told me one day a few years ago... "are you ever just driving down the road and have to fight the urge to swerve your car into a tree?"
ha...
so, hey, life is a part of death, control is a part of life, so at some point, trying to control death (in one way or another) is going to be a part of life... it's how we deal with it that counts... and being open to sharing that process with your therapist will be key to your survival if it turns out that your thoughts progress to a level you can't control
congrats on starting therapy, i'm doing so again myself within the next few months...and boy do I ever need it!!