Think about this: If you purchase something that generates more value than the cost, it's actually an investment NOT an expense. (it's a write-off!)
So take the current ticket price, divide it by 12 and ask: “Would you be willing to make a training investment in me for less than $38 per month?” (Even less if you are not planning on attending the entire 3-day conference.)
If they say “yes,” then ask, “What information do you need in order to sign off on this conference and travel expenses? Can we make it a priority to get this solidified this week so I don't miss out?"