you arrive with the published donation for "x" hour(s), perhaps find that may "2x" hours would be even better.  How do you handle the new donation, or even discuss it,  assuming provider has the time.  Seems that asking or discussing violates hobby rule number one???

You should be familiar with her hourly rates, be sure that you have enough and if she agrees to it, discreetly place the money down where she will see it.

Once you've already made a transaction and are well into the first hour, the liability of a LE sting is no longer an issue.

I've done this on a few occasions and never had a problem.

Sometimes the gal is booked up so don't always expect it.

When you say "you arrive with the published donation for "x" hour(s), perhaps find that may "2x" hours would be even better" it sounds as if you only brought enough for the time you have booked.  Am I correct?

If this is correct, then you will have to wait till the next time to book a longer appointment.

Most providers have their donations on their website.  You can easily look this up prior to the appointment and if, after meeting the lady,  you feel that you wish a longer appointment you can ask her about extending.  Just be sure you have the extra dollars with you.

Also, you can always ask in the middle of the appointment about extending.

Don't be disappointed if you are turned down.  She could have other obligations (other clients or personal business that does not allow her to extend).

I've extended a number of times, I'm running about 50/50 with providers who decline (because of a subsequent booking).  The donation is the easy part, get up to use the rest room...stop off at your pants and take out your wallet, then just leave it on the bathroom counter.  She will get the idea and then excuse herself to count/retrieve it.  Even though the LE problem is eliminated by that point I think its bad form to physically hand the provider payment or obviously lay it on the nightstand.

Well for me a lot are aware of how long they want to spend be it 30 mins, hr, 90 mins or 2hrs but i've had many time where near end of an hr guys just says I want to extend and he's familiar with my rates and goes to wherever his funds are and slides over additional moneys wherever he placed the inition donation. Depending on the girl she might or might not freaked out. If we're in the middle or a visit I can't say I'd be taken aback if asked what do I donate for x amount of time...i'll just show them my site.

Once you have already met and each others company, there is nothing wrong with asking about extending time and what the extra donation would be.

If you are already with the provider and have already paid for the first hour and started play there is no real danger in asking the lady if she can stay longer or what the donation would be for her to stay for an amount of time not advertised.  Don't expect a discounted rate, you did not pre-book this time and I believe most providers would be insulted if you expected one for just being already being there.  As for giving her money a second time it should not be a problem if either of you were LE you would not be asking to extend your appt IMHO.  
Doc