You should realize that maintaining a Thai-Western relationship takes a lot of dedication and commitment. Not only is there a language barrier, but you need to come to terms with Thai culture. Money is considered to be very important in Thai culture and as the boyfriend or husband of a Thai woman, especially as a farang, you will be expected to send her money on a regular basis (monthly?) and help out financially when there is a problem in the family - otherwise how else will she make quick cash apart from working in her bar and going with customers?
In my opinion, a lot of bar girls don't request for money in the initial stages of a potential relationship, because they don't want to scare the guy off - only when you start showing signs of love and they have you hooked is when they'll start requesting for cash.
You mentioned this girl has a son too, which you would have to take care of when school fees are due, uniform needs to be brought, etc. You also mention you make an average living - to many Thai people farang are considered rich! You plane ticket to Thailand would take many Thai people at least 6 months to 1 year to save for. Also, be aware that many Thai bar girls do have a Thai boyfriend or husband in the background, despite the fact they may say "Thai man no good".
If your serious, get her out of the bar and apply for a visitors visa for her to the UK - start off by checking out the British Embassy in Bangkok. Also, you must realize she may also have other foreign boyfriends on the scene as well as you that send her cash on a regular basis.
I strongly recommend you read the book Private Dancer which may open your eyes and bring you back down to earth.