If you do not want to take part in the sometimes inane chat with a bar girl, one alternative is to walk slowly between the two main girly bar areas of Day and Night and Nutty Park. At the corner of the road junction, is where the majority of the freelance girls work in Udon Thani, and it is normally them that will approach you.
There are not too many of these girls, but they are normally here if not otherwise busy. It is unlikely that they will be asking for the same sort of money the girls in Day & Night or Nutty Park, normally about half the amount, but sometimes a little more if they think they can get it. I have seen one or two of the these working girls on the opposite side of the busy Prakack Sillapakom Road heading towards the Central Plaza shopping mall, and again these girls will discreetly approach you to offer "boom boom".
Note I said, they will approach you - this is the opposite to the big tourist locations, where they wait for you to make the first move. Just hang around on the corner casting a glance at the girls that are nearby, and if they are freelance workers, they will come to you.
Are they safe to use? I have never tried, and have heard conflicting reports from both ferang and local tuk tuk drivers. Should you do choose this type of girl to make your night, make sure you wear protection and play safe. It is widely believed that many of these girls originated in the nearby bars but have been removed from those premises for one reason or another (generally causing problems), and in some cases are drug users. To say they are perhaps less desirable than the average bar girl, in my opinion, is not unfair. A quick glance at them should be enough to see how rough some of these girls appear.