The section of 3rd west from Asbury to the Subaru dealership can be very challenging to the cyclist because of the traffic. If you are not strong enough to sustain about 15 mph for a block or two it is reccommended that you dismount and cross 3rd in one of the crosswalks.
Although it looks like it continues on 3rd uninterupted, you will actually have to negotiate a left turn to follow the route.
This section is much improved since a center turning lane was added. Often auto traffic is going at sub-bicycle speeds, especially the eastbound lane.
The best way to navigate this section is to gain control of the westbound lane using a natural break in traffic. Wait at the stop sign and look to the left to watch the traffic at the light at Jackson St. When the light changes there will be a break in traffic. If you time it right you can pull into the curb lane on third and move to the westbound lane when the traffic break gets to you. From there move over into the left turn lane when you get to the car dealership.
Put another way, the Jackson Street light is essentially metering traffic flow, creating breaks that the cyclist can exploit to move across the westbound lane to the turn lane. Once there, the cyclist can wait for a break in the eastbound traffic if necessary.
I do this twice a day and have no trouble 9 time out of 10.

