You can use insulin straight from the fridge - I was always told that it would be more uncomfortable, but have never noticed that myself.
While my situation (using short acting insulin x 3 per day, plus long acting x2 per day, rather than your bimodal insulin, which contains some of each type) is different, the principles are the same. I always have a spare cartridge of each of the types of insulin I use out of fridge, in pencil case, which goes everywhere with me - I reasoned that I never knew when I might need to stay out overnight and didn't want to be separated from long acting left at home. It's not happened often, but was pleased to have some long acting with me when invited to go kayaking some 12 years ago - and we're still together 🙂