One Day Trip from Amman Jordan to Jerusalem sept 8th to sept 16th

Welcome to Thorn Tree.

You don't need a tour. It's easy to do it by yourself, but it's not really a day trip.

You would take public transport from Amman to the Allenby (King Hussein) Bridge, then cross the bridge - where there can be lengthy delays, which is why it's not practical for a day trip - and then take a bus or shared taxi from there to Jerusalem. Once in Jerusalem you can wander around seeing whatever you like. Do some research and plan what you want to see. Come back here for answers to specific questions.

If you want to have any time to see things in Jerusalem, you must spend at least one night there. Otherwise, you may find yourself with about only 2-3 hours (depends on delays at border) to see a city which really needs a minimum of 3 days.

You heard the facts and advice from forum veterans above.I second their views.
here is brief summery on cost if you do it alone.
Amman to Bridge $ 30 exit tax 11,bus over bridge 4,shared taxi to Jerusalem Damascus Gate 16.
same for return journey to Amman plus Israel exit tax around 40 and you come with a figure close to actual cost.
Border crossing time depends on the numbr of people crossing the bridge on a particular day.Also allow for early closing of bridge due to Firday Sat and religious days on both sides of borders.
cheers

Visiting Jerusalem from Amman as a day trip would not be a good idea; trying to do it as part of a tour would be foolish.

Tour companies offer such tours to pray on people's ignorance.

Do it yourself and devote two to three days at least.

Good luck.