well there are two ways to do it. Figure when you shift from 1st to 2nd, lets say you're at 3k rpm. For that speed 2nd gear needs to be going around 2k rpm. So either you can press in the clutch, let off the accelerator, and wait for the needle to drop and dump the clutch all at once, and hope you "time" it right so that you land right at the correct RPM. The other way is you can ease off the clutch over 2-3 seconds, and in this time the RPMs will be dropping.
Also same goes for downshifting (but backwards?). When you go from higher gear to lower gear, the revs need to be higher. So from 3rd to 2nd you need to be going sometimes 1.5 -2k higher RPM. So to "match" those when you downshift as clutch is pressed in, instead of letting off the gas, give it a blip and then let off clutch. This will match the revs to the lower gear since it will need to be going faster at the same speed.
There are many good videos about rev matching in manual transmission car. You can spend hours on youtube watching all different various techniques.
Clutch will wear when you have it slip. But IMO i think that dumping the clutch to early, or having the synchros pick up the slack by not rev matching will put more wear on the transmission than releasing the clutch slowly and reducing the jerkiness to a minimum. I like the feel of a nice smooth clutch release when you can really feel it engage all the way down. I don't know how to compare to your bike, but if you are hearing the clunk or feeling jerk then you are probably putting a lot of stress on the transmission.
A few things I advise specific to Jeep Compass manual transmission:, in the Uconnect system you can enable the parking brake to automatically engage when you turn the engine off. THis is nice feature since when you come to a stop you just have to hit the off button and get out, the brake takes care of itself.
Also if you see your manual, in the manual transmission as long as you have the seatbelt buckled, when you put it in gear (1st or reverse) if the electronic parking brake is engaged, after you give it a bit of gas (let of clutch slightly) the electronic parking brake will automatically disengage. So you don't actually have to manipulate the EPB at all if you also use above option. When doing this method you do not need to hit the brake for the EPB to disengage, just gas and let off clutch. SOmetiems I will engage EPB when I come to a long light on a hill, and when I need to go I just start off in 1st and the EPB disengage by itself. Using the EPB somewhat like an extended hill assist, but it gives your feet a rest for a bit.
2nd thing is you have Hill assist. SO when on an up-hill you can take your foot off the brake and it will hold you for about 1.5 seconds, while you clutch in and start gassing in 1st. This will also work if you reverse up a hill. This helps that you don't need to feather on the clutch/gas to keep yourself from rolling backword. If you find that your hill assist is not enabled, you can check this feature, it is not in the Uconnect but in the steering column options. I think under "safety" but I could be wrong. These are found using the dashboard cluster and the steering wheel directionpad.
3rd, I and others have commented that reverse gear is a bit high. I don't ever release fully off the clutch, especially in parking lots. Either you will stall or ram into cars. I ride the clutch 1/2 way until I'm backed up enough then into 1st gear.
edit here is link for video I liked (has camera on feet too)