How do you go about asking them to be your mentor or an advisor for you and your startup? Is it just contacting, couple of meetups and asking?
Like anything to do with a startup, it's about proactive outreach. AngelList is a great way to research what people have done before. You want to optimize for relevant experience. AngelList however is very ineffective for making cold connections. Instead, I use LinkedIn and ensure to always write a personalized introduction with my connection request explaining why my company is something they would be interested in.
After the connection is accepted, I then follow-up with a personalized email thanking them for accepting the request and then asking to buy them a coffee or schedule a meeting.
I have built a great network of both formal and informal advisors and investors through this process.
Formal advisors really should be limited to just a few. In these cases, granting options to purchase equity between 0.5 - 1% is standard for great advisors. But reimbursing expenses is far less standard. I'll always offer to pick-up the tab as a sign of respect for their time, but other than that, advisors (myself included) are generally happy to pay out-of-pocket unless for travel.
Just like any relationship, be sure that you want to make a long-term commitment in equity before formalizing the relationship. Often, good advisors where there is a mutual chemistry will be happy to do many meetings without anything committed.
Lastly, I would caution you to be wary of people who approach you to act as an advisor and/or people who are actively operational and also on many advisory boards. I limit myself to a handful of formal advisory relationships at a time and it's usually owing to a longstanding friendship that I am an advisor. You want your advisors that you're paying equity to to really be engaged.
Happy to talk any of this with you in a call.