I agree with both the above posters. Better to buy directly from Java and no Bali because most of the furniture is trucked from Java to Bali to sell. You can see big trucks packed solid with furniture on the roads anywhere between Kerobokan and Ubud coming from Java.
Yan's Antique is alright and Yan is a very nice man. He belongs to the Tabanan family which also includes Mario Antiques and Mario's wife Etsy is a charming Javanese woman who handles the sales and orders. They are both located just north of Sukawati before reaching the village of Mas. Mario's have a furniture workshop nearby with all the machines for making teak garden furniture and for updating and repairing old carved teak benches that they bring in from Malang in Java. However, even though they make much of the teak garden furniture, their prices and slightly higher than most of those companies who import from Java. If you are not really interested in garden furniture then you would be much better off looking in Jepara.
Ubudian is right about the humidity of the teak, but other things to look for are new furniture that have had little damaged pieces repaired. This is where they cut out a piece of rotten wood and replace it with a new piece, so a so-called new piece of furniture might have little squares of different coloured wood, so you need to be clear with the manufacturer that you will not accept this. Also, because furniture is a big business, a lot of young teak is being used. This is a lighter whiter coloured teak and the manufacturers stain it darker to look like the nice mature teak that we all like. Mahogany is the other popular wood and they stain it dark red-brown so these problems are less obvious. Some dishonest suppliers might try to pass mahogany off as teak, so look for the tiny holes that insects make because teak is an oily wood and repels insects. Basically, quality control will be one of your biggest problems.
I also agree that buying directly from Java is better. But you can easily go to Jepara and ask around for the bigger factories. There are literally hundreds and hundreds of furniture makers. Go and check the quality and ask around for the best places. Be aware that if you hire a driver he might ask the factory for a commission for bringing you there.
As with production of most products, quality control is essential, whether you choose to do this yourself or use an agent. Agents tend to know all the factories, but they sometimes take commissions from the factory so they will be taking it from both ends which essentially means they are also on the side of the factory to a certain extent. But a good honest agent, which might well be a foreigner, will be strict with the factory. QC needs to be done during production as well as on completion of the order. If you use an Agent pay them their commission at the end, usually anywhere between 10% up to 20%. Foreigners will ask more but they probably do a better job. If the factory asks for a deposit then try to pay about 20% max. When you are a regular customer and win their trust they will probably not ask for a deposit but it is fair to give them something at the beginning. Personally I would not use a sourcing/buying agent.
Choose a large and reputable cargo company such as Ritra Cargo/Logistics. They will do a good job packing the furniture and fumigating the container. Using a cheap low price cargo company that promises this and that may result in your furniture being packed into a container carelessly and arriving damaged. If you are shipping a full container of goods, it is a good idea to buy smaller items too so that you can fill in all the empty spaces in the container and therefore maximise the usage of the container and thereby reducing your shipping costs per item.
Good luck and have fun.