When I first started carrying 1911s, I took some very good advice (outlined above).
Even though I had owned and shot them for years, carrying one was a whole other deal.
I started out by carrying it around the house, chamber empty, hammer cocked, thumb safety on.
At the end of the first day, I found that the thumb safety was still engaged and the hammer had not fallen. Imagine that.
Day two, ditto. And so on. That was reassuring enough, at a certain point, for me to start carrying it. The fact that I shoot a 1911 better than anything else might have had something to do with it, too...
At a certain point I owned a 1911 with an ambi safety. On several occasions I found that the thumb safety was disengaged...but the hammer had still not fallen. That re-inforced the reassurance.
I got rid of the ambi safety, but still, once in a while I find that the thumb safety has become disengaged due to my daily maneuverings.
However, due to the 1911 design, the pistol is perfectly safe in the holster without the thumb safety--the grip safety is functioning, and the trigger is not being pressed. The fact that my 1911 also has an FPS is a third level of safety (although I own another without an FPS and trust it just as well).
Once you have spent some time with the 1911, and really understand the overlapping levels of safety designed into the pistol, you will be more comfortable carrying one.
It is just like any other pistol--keep your finger off the trigger and you will have no problem.
But unlike many other pistols, it has those overlapping levels of safety. It is the genius of the design that has kept it going (and growing) for 100 years.
Do some searching, reading and learning. Shoot your 1911 and when you are comfortable carrying it, do so.
There are very few handguns that compare (although that is an opinion, it is one shared by a fair number of people).