Hi,
I've never worked on a BF 150 so this might not be of any help at all for you. Just tossing it out there though just in case.
In the parts page link below there appears to be a pan head screw at the rear of the cover that could be holding it there. See item 20
Buy OEM Parts for Honda Outboard 150HP Under Cover Diagram
www.boats.net
And, although it doesn't depict a screw at the front of the cover, there is clearly a hole for one shown. That screw would likely thread into the front cover bracket. See item 5 in the link below.
Buy OEM Parts for Honda Outboard 150HP Front Cover Bracket + Front Lock Diagram
www.boats.net
Also, in the top link there is a bolt, item 14, on the inside of the cover but I don't see what it would hold or attach to.
The item 14 count calls for 6 required but that drawing only shows 2 on the left (port) cover and only the inner one on the right (stbd) side.
Hope this might shed some light...maybe....hopefully....perhaps...
But maybe not since your outboard is about 14 years newer.
Good luck