Personalising a blog invitation, is impossible with Blogger, because Blogger does not give you access to the invitation, before it is sent.
So, if you want to add a personal note, or a description of the blog, you have to send an extra email, apart from the invitation, explaining what it's for. For example, if I want to send an invitation to this blog, to a friend, I would say something like;
I am sending you an invitation to my Private blog, called 'the Blogger' blog, which concerns itself with technical aspects of blogging, which you are interested in. It covers many of the subjects we talked about, and shows you easy steps to complete them.
I hope you accept the invitation to become a reader."
To do that, I have to think outside the box. How can I personalise my invitation to Bob? There is only one way to achieve that, and it requires the use of a 3rd Party, in this case, myself.
It's the person who ACCEPTS the invitation, who becomes the Reader - not the recipient of the emailed invitation ! Remember that!
I send an invitation to myself. I copy the invitation acceptance link (URL) from the email sent by Blogger, and compose an email to Bob, adding my personalised message, and the link (URL) to the invitation. Easy as. Bob accepts. Done.
I can always delete the Reader if someone else accepts it.