Hi - if you are suffering from diverticular bleeding then there is a (slight??) risk that this can suddenly become severe - I suggest that you ask your G.I. doctor to elaborate. I would imagine that you have two choices:-
a) treat the diverticular bleeding (howsoever) and trust that you are not suddenly afflicted with a torrential bleed that could be life-threatening if you do not receive prompt medical treatment (as happened to me)
b) more drastic - undergo surgery to remove the colon (total colectomy) which eliminates the risk of severe bleeding - but exposes you to the risks and discomfort of surgery.
Do discuss this fully with your specialist.
Five years ago I underwent a total colectomy for torrential diverticular bleeding and, in response to another Medhelp patient's question, I recorded my experiences on:-
http://www.medhelp.org/posts/show/523166
You might like to print this off and show it to your specialist to see whether he/she concurs with my own experiences as a basis for reaching a decision on (a) or (b) above - or any other option that may be offered to you.
Good luck
regards
Morecambe