Again .. in terms of trademarks every situation is completely different.
Legal Side:
If your company's website is BlueBullLondon.com, but they actively use "Blue Bull" for business purposes, then their trademark would be "Blue Bull" (yes .. even if it's not a registered trademark) and you would NOT be allowed to approach them to sell BlueBull.co. Doing so would cause you to fail the 3rd step of a UDRP action which states you acquired the domain in bad faith. However, if your company always refers to itself as "Blue Bull London" (and hopefully has a registered trademark ONLY for the longer one), then you might have some wiggle room. There are too many unknown variables .. the biggest mistake you can make is asking for advice without giving the specifics .. because without specifics we're all just guessing.
Non-Legal Side:
If your company only operates within the geographical scope of London and is the type of business that isn't prone to geo expansion, then I doubt they will even want the .co. If they could potentially expand then I still think the .co is a challenge if another company exists that is actively using the .com. I'd recommend a complete name change to a different and better .com for an existing company. But again .. I'm completely guessing .. NO opinion is ever going to be relevant in any way without knowing the specific details. So do not even take my or anyone advice .. lol.
All that said .. you're probably better off not sharing the domain/company names .. that could also get you into trouble.
Good luck either way! In the future you're probably better off not registering such domains. The better thing to do would have been to approach your management first and ask them how they feel about their domain and offer to help them find a new one.
If the TM connection is confusingly fuzzy enough to not be a TM or UDRP issue, then I'd at least follow what Rob said about using a 3rd party/broker/friend so that at least you don't risk losing your job!
ADDED:
The reality is you probably did management a favor
At the end of the day .. if you forget the legal side of things .. what Rob said is probably the closest thing to reality. With the only real problem being whether or not management is competent and knowledgeable enough on branding and domains to even understand the favour? lol .. I've seen some very high-up executives decline even discussing the topic of domains simply because they not only don't see the value .. they don't even understand them to begin with.