I have offered a 50 point bounty for answering one of my questions. Someone responded with a suitable answer, but because I was late to respond this person received only the community assigned half. I have now accepted his/her answer and wish to award the remaining 25 reputation points, but cannot figure out how to do this. I remember there was an option to do this when offering a bounty but when I now click it I only get 100 or 200 points as options.
You can't. What happened is the bounty was auto-awarded, meaning they get half the points (and the other half of the points rae gone forever). You can start a new bounty and give it to the same post manually, but the minimum cost for bounties increases each time you use one for the same question up until it costs 500 points per bounty.
See also How does the bounty system work?