There’s really no reason to add an extra 3/4 mile walk, or a transfer to a bus on Adams.
Luggage. Plus, the bus drops you right across the street from Union Station entrance/exit. And the escalator at Clinton is narrow. And, if you want the elevator. Depending upon bus connections/traffic, you might even be at Union Station by the time you get up the stairs at Clinton. And, maybe you want to grab something to eat in the Loop.
Given, if you're just taking Metra and carrying nothing, Clinton can be worthwhile.
If headed to Ogilvie, sure. It’s a longer walk from Clinton (Blue) and the buses on Madison are more frequent.
There are numerous routed on both streets. You, usually, won't wait more than 10 minutes during the day, often less.
I have less faith in the frequency of bus service along Adams not making such move a complete waste of time, except maybe during rush hour. If you’re getting into downtown at 6 or 6:30 am as the person a few messages up is probably doing, it’s not going to be rush hour yet. And if you’re unfamiliar with the area, it’s a lot easier to find your way through the block and a half from the Clinton (Blue) stop to CUS than figuring out which exit to use from the quarter-mile-long Blue Line platform that can put you on the surface a block or more from the actual street the station was named after, and then figure out which bus stop to go to.
Apps help. And there's plenty of signage. Plus, people here.
Coming from O'Hare? Walk towards the platform exit at the front of the train at the Monroe stop. Stay left and straight ahead at the Mezzanine level. At street level, walk to the corner straight ahead and turn left. Your bus stop is just down the block in sight.
Alighting at Jackson? Walk towards the rear of your arriving train after you alight. You can can take the elevator or escalator to mezzanine level. Exit the fare area. Take the elevator up to the steeet or stay right and walk up the stairs. Continue half a block to Adams. Cross the street. Turn right, the bus stop is down the block.
So basically, straight ahead and left or behind you and right, depending which stop you choose. Easy peasy.