I would take the OCTA Route 543 northbound up to Harbor to the Fullerton Train Station. $ 2 per person, or if you have a valid ART pass, that also works for OCTA.
Catch the Metrolink to LA Union Station, buy a weekend Day pass for $10 from the vending machines at the station.
Take the LA Metro Subway (Red or Purple line) to the 7th Street Metro Station, and then just walk a few blocks to the LA Convention Center. (Your Metrolink Train ticket works for the fare, just tap the ticket (it does have a chip embedded in the cardboard).
To return, reverse the trip, the Weekend Pass works on all three segments including the OCTA.
Just watch the train schedules, as they only run a few times per day.
http://www.metrolinktrains.com/sche...m=97&to=131&weekday=0&submit.x=39&submit.y=17
http://www.metrolinktrains.com/sche...m=131&to=97&weekday=0&submit.x=99&submit.y=10
If you miss the last train (around 7 PM return), you could opt to take AMTRAK, its last train leaves Union Station around 10 PM. That would be an extra fare.
Or opt for the LA Metro Route 460 on the way back, and your Metrolink Day Pass will work on the bus.
Or if you truly want to be cheap, you could just take the LA Metro Route 460 bus. Get to the Main
Disneyland Bus Stop (under the Monorail tracks) and catch the bus there. It leaves every 30 minutes, and would be about 90 minutes before getting off at Pico, next to the Convention Center, its last bus back is just after 10 PM. You needto tell the Bus Driver when boarding that you want a round trip ticket to the Convention Center, and ask how much it is,since Route 460 is one of a very few zoned routes, there might be a surcharge above and beyond the cost of the ticket (base fare is $1.75 each way), so make sure you have Dollar bills and some pocket change (such as a few dollar in quarters, and a few nickels and/or dime), so you will need to pay when you board going both ways
So those are two good options, I would opt for the Train personally, at least going to the event, maybe opt for the bus going back, depending on when it wraps up.