Should I "offer" something when asking for a letter of recommendation?
Just straight up ask for the letter.  There is no need to "pay back" with some favor.  Writing letters of recommendation is part of a supervisor's job.  However, it would be wise to include in your email:


Position description so they can describe the most applicable aspects of your prior work in their letter
Ask if they would be willing to write a "positive letter of recommendation" because if it is not positive, they should not write it
Information about: where to send the letter, to whom it should be addressed, and the date when the letter is due
Ask if they would like you to send a reminder email 2 weeks and also 2 days prior to the letter of recommendation due date


Additionally, if it has been some time since you spoke to this person or you do not know if they remember you, include your latest CV or Resume with your email. You should never have to draft your own letter of recommendation.  I highly look down on this practice, though you may encounter it.