bus from Dublin airport to Trinity College Main Gate

I don't think you can do it in one shot. The 747(?) bus will take you to the lower end of O'Connel Steet for five or six euros. From there it's a five minute walk across the bridge to Trinity College. If you don't want to hoof it, since you will have been dropped right in front of the main bus office, wander in and ask them. There's a zillion busses that stop in front of the college.

The road on the south side of the river is one way going west (sort of). I think the Airlink 748 bus can drop you off within 2 or 3 blocks of Trinity. That will cost about 6 euro per person. A cab will get you to the front gate from the airport for about 30 euro for up to 4 people.

At the airport ask the person at the ticket machine. They'll help you get on the right bus. Confirm with the driver which stop you want to be close to Trinity.

The bus is fast and convenient. Unless there are four in your group, you'll save money.

Let me check my ticket. One of them drops off right outside the gate, you tell them Trinity and that's what the ticket even says.

Found it. Aircoach, Dublin Airport to Trinity College, 7 Euro, last August. I went outside the airport, they were set up outside the main doors, paid, hopped on, then got off at Trinity.