You need to be systematic about this.
Take the cleanest, freshest clothes you have in your suitcase and wear these home. Don't wear old clothes as bedbugs like the smells.
Put the suitcase and bags in the boot, not on the seats.
Pop to the shops on the way back and buy large bin bags.
You could sit on one on the way back the rest of the way to minimise the chance of any getting in the seats...
Put the suitcase and all clothes in the bin bags and tie them. Leave them outside for now. Strip off to underwear or get naked before entering the house.
Shower, refresh, etc (you'll probably need it!).
When you're done, take a few binbags and go outside. Stand a little bit away from your suitcase (to be safe) and separate clothes into darks, whites etc. Put these into the bin bags and tie them.
Take these in, and very carefully tip them into the wash and put them on the highest heat wash possible, and dry on the highest heat possible.
For delicates (shouldn't be many), put into small bags and freeze, then wash as normal.
For the suitcase, I'd probably buy a mini steam cleaner (amazon for about £30). Be thorough. Use this to steam clean the boot and passenger seats of the car (hopefully not leather!).