Of course you can rebid.
Longer answer: would-be investors (at any age) tend to run into a lot of nay-sayers, generally beginning with their families. That's not to say they don't have your best interests at heart; I'm sure they do. But people have an inbuilt resistance to things they don't understand or that they haven't done.
So, here's what you do. Assemble a "team." That means a Realtor familiar with the process (you may already have that) and who can tell you what the house would be worth once the work is complete.
You may need a lender. Get some recommendations from your agent. If it's going to be your primary residence, look into 203(k) loans--they're FHA loans that bundle the purchase price and the rehab cost.
You need an accountant. Look into your eligibility as a "first time home buyer" for the tax credit. People who haven't owned a primary residence in 3 years may qualify. AND people who've owned a home for 8 or more years and lived in it continuously for 5 or more years may qualify. Here's a link to the IRS web site: bit.ly/HomeBuyerTaxCredit
You need a construction person--someone to give you a good idea of the repairs the property needs. If you're going to be living there yourself, you know what you'd like and what you wouldn't. If you're planning on reselling it, consult with your Realtor on what amenities and improvements will best help sell your home. And if you're planning on renting it, again consult with your Realtor but don't overimprove the home. Rehabbing for rental is quite different than rehabbing for a sale.
The fact that the house needs too much work, is too old, and too dirty is great. It means that those same factors will turn off (and have turned off) would-be buyers. There are plenty of things that scare off people that are really easy and inexpensive to correct. So, that's why you need a contractor to tell you what things will really cost.
Finally, in today's world, 68 isn't too old. You may have another 10-20 years of vigorous activity ahead. (Hey, my uncle is 94. He plays tennis three times a week. He just wrote a book. You're barely getting started!)
So, you assemble a team. That, in itself, will help offset the criticism and negativity of your well-meaning family.
Go for it!
You are the offeror and you need to offer what ou think it is worth. I would suggest you consult a licensed professional so they can estimate the fair market value for you. They should be able to give you a range (pristine to lots of work) I'd also encourage you to conceder Structural, functional and cosmetic issues. A dirty home can be cleaned, walls can be painted the color you want and flooring can be cleaned or replaced. During the inspection period, you hire an Home Inspector. They give you a report on all the functional and structural issues. Then you get bids by contractors so you know what it will take to correct the problems.
Let me know if you need referrals.
Realty World Superstars
Long Realty Company
Tucson, Az 85704