Dulles transportation to Hyatt Regency Capitol Hill
 

What is the best way to go taking Metro bus 5A to Metro station and then railing it over or just grabbing the Super Shuttle (other options)? The Metro will take about $12 RT and the Super Shuttle about $65. I want to do it in under an hour and a half. Thanks.

The day of the week and time of travel (rush or not) will have some bearing on your decision. 1.5 hours isn't unreasonable but not a guarantee in peak traffic times.

Don't take Super Shuttle if you want to do it in less than an hour and a half. As Obxgirl says, the bus will matter based on what time you are arriving since. A taxi will be about the same prices as SuperShuttle.

Was that $65 RT for SuperShuttle? If so, double that for taxi as it would be close to $60 each way.
Rather than going from bus to metro and changing trains at Metro center, you could take the 5A to L'Enfant Plaza and hail a taxi from there to the hotel for about $6 one way (a bit more in slow moving rush hour traffic, of course).

My plane arrives at 3:39 PM and I suspect I will be ready to board the bus around 4ish. How would the traffic be at that time? Probably bad right? In LA it would be bad.

Yes, if that's a weekday arrival time, you'll definitely be in traffic. But an hour and a half transit time isn't out of the question. I'd pass on the SS since you won't know how many stops are between you and your hotel.

At 4PM on a weekday??? Get ready for a whole LOT of traffic, which BOTH the taxi and any shuttle will have to get through, especially if they are using the I-66 eastbound approach.

Personally, you might consider taking a TAXI to the nearest Metro stop and THEN taking the Metro