I personally do not think, USA has offered BD a physical presence of US troops along the BD border. However, a few years ago USA sent a team to survey the BD-India border. As far as I understand USA has installed some kind of listening/watching equipments across the BD-India as well as BD-Burna border.
The then US Ambassador defended this action by saying that these are to check infiltrators (read terrorists) across the border. US has also installed two radars in Kuakata and Cox's Bazaar. These the US says is to watch over the sea pirates. Well, to US and BD India itself is a pirate.
USA uses many vague and diplomatic words to camoflage its true intention. However, I believe the already installed border equipments are to check the movement of Indian and Burmese troops. The shore radars are to watch also Indian and Burmese navy movements.
Not only this, USA has installed also a number of watching equipments on Himalayan tops and in Arunachal Pradesh in order to watch over any Chinese troop movements. But, I think these are also to watch over IA troop movement. This is how the Policeman of the world polices different potential conflict zones.
Therefore, I believe, US does not intend to man our border along with BGB with a physical presence. Rather, it wants to install many more watchdog equipment posts along the border to watch over Indian troop movements.
I have reasons to believe that it was the USA who had informed BD in 2008 of the Burmese survey ships in an area which lies only 32 km SW of St. Martin. When BD sent its naval ships to the contested sea, one US navy ship has already arrived and anchored in CTG, all in the name of humanitarian assistance to the cyclone victims. But, it was too quick. It means it sailed for CTG immediately after the USA had notified BD about the Burmese activities.
We have to understand that any point in the sea is very difficult to pinpoint correctly without sophisticated aerial survey equipments. BD does not possess such equipments. But, US satellites are capable to pinpoint an X-Y co-ordinate in the sea quite accurately. This is how US came to know about Burmese movement near St. Martin which it informed immediately to the GoB. Reality is USA is already working with BD military for quite a long time.
Considering all these I am of the opinion that US wants to install many more listening posts along the BD border with India and Burma. It certainly cannot watch China from BD. To watch over China it already has a few watch posts on the Himalayan top.
Sorry for the long post. It is indeed too long. But, I thought I better share the information which I have gathered during the last few years.