Anyone know Danish company BPS M?  

There will probably not be much more information on your table if it is not listed in the archive that posted by the family. The company did not work with outside architects/designers.
The Vamo chairs, which you haven't shown in the photos, are by a completely different Danish company (Vamo). They were probably purchased at the same time at the same retailer to go with the table, as obviously Danish Modern teak pieces go quite well together in general, even if they are not from the same company/designer. They are like either Arne Vodder and Anton Borg or Johannes Andersen, or possibly Torbjørn Afdal chairs, as these were the designers most known to have worked with Vamo.
If you post a photo of the chairs, I would be happy to tell you what they are. There is a high chance that I know.

Thank you! I'm thinking possibly my table maybe 158 or 149,but my tape measure is missing in action.I will have to measure to possibly be sure.Thanks for the insight on the company not working with outside designers/architects.Yes the chairs compliment the table beautifully.They have alot of the same design lines.They have been recovered,so not original covering.Thankful for any insight on these beautiful pieces.

I just noticed something interesting: Koen said that he did not think that Bernhard Pedersen ever worked with any designers of note. I've taken that as gospel for lack of evidence for a long time. But it is no longer completely true.
This model (model 160, which is actually a whole dining suite) posted further up the thread was designed by Johannes Andersen:

I can confirm that Bernhard Pedersen & Son worked together with several architects - for example Johannes Andersen and Kurt Østervig (In the 1960s, one of Kurt Østervig's designs was exhibited at the Museum of Modern Art in New York). Two days ago I actually talked with Kurts son (Mogens Østervig) and he was very pleased to hear that I had some of his farhers original drawings of a daybed (model 159). In almost a decade, that daybed was a huge success.
I'm also trying to find some relatives of Johannes Andersen but so far without any success. There is very little information about Johannes Andersen so if you have any information, then please let me know. I know that he also designed furniture for Uldum and Silkeborg Furniture and according to google he later started his own factory in Farum (north of Copenhagen) but this might be incorrect.
I have searched old newspapers, visited the library at Danish Design Museum and last week I spoke with architect Jørgen Bækmark (who worked together with Børge Mogensen at FDB furniture) and architect Bodil Kjær. Very interesting talking with them (I could talk with them for hours) but they didn't have any details about the 'less known' architects.
Bernhard Pedersen & Son also designed furniture on their own and many of those also had great success.

Very interesting.
So "model 160" is actually a dining suite, including the long sideboard, a tall sideboard, a dining table, and dining chairs. Are these all Johannes Andersen? Or just the sideboards?
And then model 162 is a long sideboard with the same handles, is it an in-house design?

The above chairs, credenza and sideboard are designed by Johannes Andersen 🙂 and yes, Model 162 is in-house.

Did Johannes Andersen design any other models for Bernhard Pedersen?
And did Kurt Østervig design any others beyond mdoel 159?
I don't really think either of these designers is particularly less known. Compared to Wegner, Jacobsen, and Juhl, sure, but there are many more, much less known Danish designers than these two.

Here is model 159, just to keep this information together.

Another question: were the copyrights to these models owned by the company, not the two designers?
It is an odd question, but I have been researching some other pieces of furniture where the designers did not have a design credit in the maker's catalog, and the BPS catalog is like this. My guess is that it has something to with whether the maker or the designer owns the copyright to the design, and I am hoping you might be able to fill me in with some detail.

Its my grandfather who ran the business and I don't have such details.
Johannes Andersen also designed other models for Bernhard Pedersen & Son and the company also worked together with other architects.
Do you have any information about Johannes Andersen, ie. what he did after 1965 ?

According to the Danish Furniture Index, Johannes Andersen was still designing furniture in 1968. And I have noticed that it is harder to find documentation on Danish pieces from later than about 1968-70. I assume the downturn in the business is related to this. So I think it is entirely possible that Johannes Andersen continued designing furniture for a long while.
I would be very curious to know who designed which models in the BPS catalog...

"I would be very curious to know who designed which models in the BPS catalog..."
Me too. The first piece of Danish Modern in my house was (and still is) the 188 credenza with 160 hutch.
Coincidentally, I was also looking at a similar-styled Johannes Andersen Uldum credenza to buy at the same time, but the total cost including shipping was above my price range.
It would be funny if the BPS credenza I bought ended up being JA designed after all.