What measurements do I need to transfer the fit of my home bike to a rental, or at least close enough?

As I travel I like to ride. But it isn't feasible to take my bike with me. So I will rent. Rentals will probably be whatever is available. In the past the shop has been willing to install pedals and make adjustments, but that is it.

Basic: Reach. saddle to bars, that includes top tube length, and stem extension..

and Height, the pedal to seat top , for leg length , 'size' of frame/seat-tube length + seat post extension..

bring a tape measure ..

Thanks. That is what I thought at first glance. But I didn't KNOW. Now I do. Thanks

The Park Tool website (parktool.com) has a form you can use to record all the vital information on your bike's setup, they have them for road, time trial and mountain bikes. It makes this process easier. The road version is here: https://www.parktool.com/uploads/file...sitionroad.pdf

you might also want to get the "saddle nose to BB" measurement. Once you've gotten the saddle height set close, gettting the saddle into the similar fore/aft position will put you closer to where you were on the old bike. You're actually concerned with the sitzbone placement relative to the crank/BB position, but since most road saddles are within a few mm of length, saddle nose to bb is the easier measurement. CAVEAT might be some of the newer saddle shapes like the Adamo...
to measure : make certain that the bike is on level ground (even a 'flat' concrete surface may not be level - my garage floor slopes markedly from front to back)
drop a plumb line from the saddle nose, making sure to allow the line to properly find 'plumb', letting it hang against the crankarm can cause it to not hang properly.
measure from the hanging line, in a horizontal plane, to the center of the BB/crankarm
replicate on the new bike - making slight adjustments for any change in crankarm length from old to new...

Saddle height above center of pedal spindle along seat tube,
saddle vertical height above ground,
handlebar top vertical height above ground,
Those will let you set up the saddle vertical position and the drop or rise to the handlebar.

distance from front of brake hood to point where saddle top intersects axis of seat tube,
horizontal distance from nose of saddle to a plumb line down to the BB center (bike must be level).

Also, saddle length, stem length, and handlebar reach may be useful.

This should let you transfer contact point locations from bike to bike.

I hope I haven't gone overboard.

Not at all for a complete transfer. I've not done a lot of renting. But, what I have the shop hasn't wanted to change stems, cranks, etc. to completely match my own bike. But, I think the "best fit" changes over time so adapting to a rental bike isn't that big a problem as long as it gets adjusted close.

Thanks everyone.