Generally, attach your resume when emailing bankers for networking purposes. Bankers receive many messages from students, and your resume lets them quickly understand your school, experience, interests, and potential connection to their group. It can answer basic questions that would otherwise require several emails.
Including a resume does not mean you must ask for an interview or referral. Your email can still request a brief informational conversation. Think of the resume as useful background material rather than the main purpose of your outreach.
There are limited exceptions. Do not attach it if the recipient or a networking program specifically says not to send attachments. You might also omit it from a casual introduction made by someone who has asked you to send only a quick note. If you are uncertain, however, attaching a concise PDF resume is usually the more practical choice.
An attachment can occasionally be caught by a company’s security filter, particularly if the file format or filename looks unusual. That possibility is not a reason to avoid attachments altogether. Use a standard PDF, keep the file small, and make sure the important message is still visible in the email body.