A riflescope would probably be more accurate and enjoyable to use than the BSA red dot scope. At least it would be to me.
The BSA may or may not hold up to the recoil for very long.
In very cold weather the red dot battery can lose it's power more rapidly too.
Sometimes the dot can be hard to see in strong sun light.
There was a state or two that previously outlawed any magnified scope besides 1x that legalized the use of magnified riflescopes as recently as within the last year or two.
There were quite a few used 1X scopes for sale at that time and there still may be on places like eBay and in private classifieds.
TC made a very nice 1X riflescope with a 32mm objective lens.
There are others too some of which are more expensive yet only have about a 20 - 25mm objective lens.
One is Sightron and the other is a Nikon.
One of the least expensive 1X32mm scopes has the Traditions name on it which can be purchased directly from them.
There are also higher quality red dot scopes than BSA and some folks do like to use them.
The dot size can be important to some for long distance shooting and there are different reticle styles to choose from.
The advantage of the 1X scope is that its reticle provides for pinpoint aiming and accuracy whereas a red dot can have 3 to 5 minute dot that covers a larger area making its accuracy not as pinpoint.
The TC Hurricane Hunter 1X is one of the few that's clear with a good quality lens for under $100 used.
I would look for one of those high and low on eBay, Gunbroker and want ads.
The Traditions will work too but the one I looked through had just a little bit of fishbowl distortion but that doesn't mean that they're all that way. But for the low price it will work and it has a good field of view.
Of course the Nikon and Sightron will work too if you don't mind the spending the extra money.
Here'a list of 1X scopes on NextTag. The TC costs $125 and the Traditions costs $24.
http://www.nextag.com/1x-scope/stores-html
Here's a thread that discusses them both and the Traditions was well liked by the person who bought it and posted photos of targets that he fired:
http://www.nodakoutdoors.com/forums/viewtopic.php?f=97&t=46490
Good luck and please let us know how it works out.