Is it appropriate for a graduate student to ask faculty whether they would like assistance in writing a grant?
On the one hand, bid writing is a laborious and unforgiving activity, so any offer of help, one would hope, would be gratefully accepted; on the other hand, bid proposals do need to be written correctly and a lot rides on their success, so you are likely to encounter colleagues who are very possessive over them.

Offer to assist would likely be taken more positively than offering to write - and this could involve all sorts of things, attending and minuting meetings with stakeholders, working with administrators to develop costings, doing legwork around gathering information needed for the bid as well as drafting an argument and a case.

How to offer your services?

This will depend upon the culture within your department, however if a research coordinator or other kind of support officer is employed, perhaps they would be someone to approach first.  They would be immersed in the network in your dept and will know what's coming up.

I'd dissuade you from sending a round-robin email as this would just be annoying; an informal/social offer of help might work better - perhaps your supervisor could point you in the direction of someone currently or about to work on a bid?