I have an old remington bug ****** model BS1 which used a rechargeable battery for its power. Where can I obtain a replacement for this battery or where can this unit be repaired???

The rechargeable battery has failed. They need to be used, charged, discharged and recharged on a regular basis. If you don't, the internal makeup up of the battery damages itself.

If you are going to use it, you can replace the battery, if not discard it or replace the battery and sell it on eBay as 'Refurbished'.

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Replacing Remington and Norelco Shaver Batteries Lee Devlin Website

How old is it? many of the Nicad and Nimi batteries of old held less and less of a charge as they get older.

If you leave the batteries in the charger with the mains power turned off then the batteries are probably being drained by the charger. Get new batteries and when flat (only flat not just used or part flat) recharge fully then remove from the charger unit. Rechargeable batteries have a habit of developing a memory as if you recharge a part charged battery then it will only recharge to that flat point

You can buy replacement batteries for model R970 at shaveroutlet.com. See link below. You will need to order two

http://shaveroutlet.com/shaver-replacement-parts/batteries/shaver-battery-pack-for-most-shavers-p-211.html

This model was not made to have the batteries replaced. It is possible but the shaver body will probably come out very scarred in the process. Instead, the following replacement is suggested

http://shaveroutlet.com/remington-ms32700-lower-unit-p-210.html

Most likely, the rechargeable batteries need replaced. This model does not run directly from the cord. You can change them yourself if you can do some light soldering.
To replace them, you will need to remove screws on the back to take off the back cover. You can then remove the old batteries.

Batteries can be purchased at shaveroutlet.com. See link below

http://shaveroutlet.com/shaver-battery-pack-for-most-shavers-p-211.html

Surfing the internet is the best way to find the battery. Here's a link which might be a place you could start your search:

http://spendoo.com/1496-buy-shaving-appliances.htm

You may have to remove the battery and use the part number in your search.

It's not extremely difficult to replace the battery. There may be solder connections to deal with.