Bucharest on a Sunday

If i turn up in Bucharest on a Sunday, will there be plenty to do

Yes.

...and things be open, or will everything be shut down (e.g. transport, bars)?

Everything, especially bars and restaurants, will be open; public transport is slightly less frequent than on a weekday, but it's still reasonably good.

I'm definitely going but don't know whether to turn up on Sunday am or Monday am.

On Sunday, definitely.

cheers mate, Sunday it is then!

Sunday is better than Monday as many of the museums are closed on Mondays. Many smaller shops are closed on Sundays but the malls and supermarkets are all open if you need anything. Bars, beers gardens and restaurants are almost all open.