planko nailed the fares/ventra card stuff, but let me add scheduling. The 134/135/136 only run during weekday rush hours and only in the rush direction. ie, you can get from the Hyatt to Clark/Lake in the morning or Clark/Lake to the Hyatt in the evening. If you are trying to get from the Hyatt to Clark/Lake in the morning, the buses may be jammed, as the Hyatt is the second stop after the express portion of the route. I used to ride the 135 regularly and it would be standing-room-only while on Lake Shore Drive and wouldn't start clearing until Michigan or State.

What day/time do you need to get to the Blue Line? Am I correct to presume you'd be going to ORD to catch a flight? Your best bet would probably to get the 6, take it to State/Washington, then walk a block east on Washington to Dearborn and catch the Blue Line there.