Is it appropriate for a graduate student to ask faculty whether they would like assistance in writing a grant? I am a Ph.D. student who will be graduating sometime in May 2018. I am hoping to apply to the academic job market in Fall 2017. My goal is to obtain a tenure-track assistant professorship position at an R1 university in a field within computer science and/or statistics.

I recently looked at job descriptions, and found that evidence of grant-writing abilities is highly-valued, especially at R1 universities. I took a short course in preparing future faculty, and the instructor recommended that we ask faculty members in our department if we can help them write a grant. He said that most professors would be happy to have a student help write the grant.

I do feel that I am not a particularly competitive candidate, but that having grant-writing experience would give my CV an edge. However, I do not know what to make of this advice. I do not know if it is acceptable to ask faculty members about this. I do not want to offend anyone, and do not know how to approach it with etiquette and respect. I also do not know if faculty members would even find that advantageous to them - especially if the student is not familiar with their work or writing grants in general.

Would it be wise of me to ask faculty members in my department, as the instructor advised? If so, are there things I should avoid? Things I should be sure to do? Ways to ensure I would receive "credit", "authorship", or at least ways to place it meaningfully on my CV?
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?