The only way I can think of speeding things up a bit is if you have a long work space/counter and your bouquets are going to be roughly the same design, it's a matter of layering. Have all your cut flowers in containers according to variety. Put a cut lengths of raffia ribbon or... whatever you tie your bunches together with, spaced out along the counter. Make one bouquet up then whip along copying the order in how you have made the first, tallest at the back, if it's a sunflower do all the sunflowers, then do all the next flower and so on. When finished tie the raffia in a bow, the bouquets will all be front facing but your customers can take them home and arrange them whichever way they prefer.
Why is a calf roping contest seem to be floating through my head LOL. I think if you have an area where you can arrange them on a flat surface it will go much quicker.

Annette

You get faster with practice. I would have to agree with Annette, but also add that before you containerize your cut flowers which are ready for arranging, you will need to have them already processed - remove your leaves and stems as you need them for your arrangement (naked stems take up less room in your vases when you travel). Another trick is to process all of one kind of flower at one time and then make sure the stems are arranged (simply grabbing them usually works) so that you get only on get only one out of the group that you want while you are working. Again, naked stems don't catch so easily and pull other flowers out.
This really will make everything go so much faster and smoother. Processing the flowers will take up time, but you'll get faster at that each time. You should be able to pick and process quite a few flowers in an hour and then spend about 1/2 an hour making bouquets and having quite a few ready. At this point I figure I could make (and do, frequently) about 20 bouquets in 1-2 hours.
And I don't do them every week (but very frequently).

GGG

You might let the customers choose which flowers they want in their mixed bouquets. You could give them a choice of say five types for one medium size bouquet. Tell them that is fifteen stems, or whatever the number of stems is which you normally put in your mixed bouquets. You could probably have more flowers in your selling space if the bouqets aren't already mixed. When people see you interacting at length with customers, I think it would draw more attention to your stand.

Maybe your daughter would like to contribute some homemade cookies, as an additional selling/interest point. Can you put out bushel baskets of apples, when they come into season? Apples can be quite attractive and you could set a basket on the ground halfway beneath your table in front. You could sell them for twenty-five cents an apple--meant as snacks for the shoppers.

As for stripping the leaves from the stems. I would do that in the garden. You won't have to clean up the mess!

How about a used book exchange, just to draw people to your table? Of course, nobody would have a book to swap for the first couple of weeks until they get used to the idea.
Lorna

Thin-man...take your camera with you to market next weekend. I'm dying to see pictures of your stall and all the pretty flowers! Pleeeeeeeese.
Vikki

I knew I could count on cottagers to know what to do. It sounds like I need to streamline my method by laying things out better, giving myself more room to work, and just keep practicing. I do strip the stems in the field, so at least I have been doing that right.

Annette - I like your idea of having all the flowers placed facing the front so that the customer can arrange them at home later. That would speed things up a lot for me, but I had been thinking that customers need to see a finished product. Maybe I'll make one that looks finished for display, and then just bunch the rest as you mentioned. Probably my first customer will want the finished one, but even so, I should be able to whip up another one pretty fast if all the right stems are already in the jar. I will be thinking about calf roping the next time I do them. :-)

GGG - I have something to shoot for now - ten to twenty per hour. Zowie! That would be amazing. When you said 'process all of one kind of flower at a time', did you mean, for example, place all the sunflowers, then place all the zinnias, then all the cosmos ...? Kind of assembly line style?

Lorna - I enjoy interacting with the customers but I have a tough time carrying on a conversation and trying to build a bouquet at the same time - not enough experience yet, I think. They just slow me down even more.

The apples or cookies sound like fun, but market rules don't allow me to do that, and the book exchange idea would also be nixed.

Vikki - I'll really try. I will have to shoot a picture first thing, before my bouquet stock gets depleted.

Thank you all very much for your help.

ThinMan

Besides seeing photos of your market, I'd love to see photos of your cutting gardens!