All bowed stirng instruments do this: as you apply the pressure to the string and until it 'settles' to normal vibration it usually is sharp for a moment. You can reduce it by not putting too much energy into the string. If you have the bow at the heel and rest it on a stirng, you should find that you can in fact pull the string a fair distance before it overcomes the resistance of the rosin on the hair.
Strings are sensitive to temperature - how much so depends on how they are made and to some extend on the quality of the set-up of the instrument. You need the right level of elasticity and tension for your strings for the set-up of the instrument (e.g. neck/finger board angle, bridge height). My cello experience is that some stirngs are extremely stable. The Jargar stirngs on my previous cello were extremely stable. The stirngs on my German cello (Larson and Spirocore) are not as stable. This is because they are more elastic and are more sensitive to temperature change. Taking the cello out of a cold car, they tnd to be sharp because they've shrunk slightly. In warm weather, they go flat as the strings lengthen.
Although bass strings are much heavier, they will still exhibit this behaviour to some extent.