This solicitors' site gives some good information and examples relating to legal causality - and in particular the difference between causality and the opportunity to suffer loss.
The bicycle owner may have a claim against the owner of the garage if it could be shown there was a reasonable expectation of security. Factors affecting this would include whether the bicycle owner had been made aware the garage was no longer secure (and the manner in which they were advised : hand delivered letters to residents or their flats would work in the garage owner's favour. A big sign saying "This door is not secure" would not), whether the garage owner had offered alternative storage or advice (such as "keep it in your flat"), and whether the action taken by the garage owner was really the only - or most reasonable - course.
In turn, the garage owner may be able to take further action against the driver to recover the damages of that legal action. Factors in this case would include whether the driver could be held accountable for the bicycle owner or garage owner's responses to the incident, and include those points in the paragraph above. This is likely to be where a break in causation occurs.
The question uses the word "careless" - it's worth mentioning that "There was an accident" is not sufficient to establish carelessness, but if there was a specific legally established carelessness this could be relevant in the garage owner's case against the driver.
The bicycle owner is unlikely to be be successful in an attempt to to take direct legal action against the driver or the driver's insurer - unless it can be shown that they were the thief.