Yes you problem is almost certainly the quality of your bowsaw, I had the exact same issue with my 30" bowsaw. You need a good frame that tensions the blade and a good blade, either being second-rate will cause a problem.
Since this post:
best-bow-saws-t96274.html I have used the 1950s Tyzack Elephant saws like Bugbear, they are the best frames you will get! I found a few at car boots and they pop up on eBay every now and again.
Tyzack & Sons Bowsaw by
Rhyolith, on Flickr
Tyzack & Sons Bowsaw by
Rhyolith, on Flickr
You need a good blade too though. I used cheap (£5.00) Bahco blades from the local discount store for a while, until I worked out they were likely B grade versions and what was possibly causing my curved cuts with the 30" saw above. Using the more expensive (price was the only noticeable difference) from the local tool shop in Norwich resulted in a big improved, so I reckon Bahco does pump out B and A grade blades. A grade Bahco blades are the best blades I have tried, so the problem is telling them apart from the B grade, basically go to a reputable tool store and pay £8-10 each, then chances are its a A-grade.
Though I will still say, I have never managed to get 30" bowsaw to cut as well as my 23", I think with the longer saws everything has to be just perfect.
I have found with bowsaws that sharpness is not that important, I have use the same blade on my 23" for (I think) 2 years of heavy use and its still great despite the blade clearly being blunt. Blade tension, strength and saw tooth set are way more important. Its what makes them superior to silky saws in my opinion, they can take blunting dirt, nails, wood and all manner of stuff ecountered in the outdoors without a massive drop in performance.
If you don't want the hassle of finding a secondhand Tyzack frame, then the premium Bahco frames are the best option new (that I have tried). You can get them in most decent tool shops or garden centres. I have not come across the same B & A grade issues with those.
Something else: Bahco sell Green and Dry wood blades, its worth getting the one specialised for what you need.