Wow you guys. You sure told him!
FWIW Mike, putting a bipod on the barrel band is NOT an option, for a number of reasons, not the least of which is the resulting accuracy would probably be so bad as to make you reconsider off-hand shots!
The already posted responses (however grumpy) regarding shooting sticks, etc. are probably the best way for you to go. And from what you wrote, I do not think you were really looking for a "long distance" shooting aid, just something to help steady your shot; in that case the various shooting sticks are a great choice.
Now, if you are actually looking to make the most accurate shot possible, then there really is no substitute for a rock solid bipod in a hunting situation. In that case, your only practical attachment option is to add a swivel stud to your #1's forearm.
Even though Leeper, Cat and BUM will probably never talk to me again for admitting this, I have done just that (added a stud) to my #1-H in 375 H&H. With the bipod attached that 375 is a 400 yard rifle (I can regularly hit clays at that distance with 260 grain NBTs). Shooting of sticks, I would be less comfortable, say to 2-250, but that is only because I do very little shooting off sticks.
I apologize to all for disgracing my #1 with a bipod. I guess I shouldn't mention my #1-V 22-250 that I use for yotes, since it wears a 1A2-25 all the time. Nor should I probably mention the 535 yard yote from a couple years back...
However! I do agree that a 303 #1 should not, EVER, wear a bipod. Some things are just not done.