I've done MIA-BOG a few times, but usually with AV (who I can heartily recommend, by the way) rather than AA, so here are a few thoughts...

LHR-MIA-BOG is fine, but MIA is a hole as always (and the bit serving the latin american flights is particularly bad). I would strongly suggest that you fly F on AA (or even better Ejecutiva on AV) for the Colombian sectors if possible - I love Latin America, but the flights can be a real scrum (think AZ domestic for ambience in the back... )

The security at BOG is extremely tight as you would expect - yet another reason to go F if possible. The only serious drawback of going via MIA is on the return - US customs are deeply suspicious of anyone travelling from BOG (even if obviously European and carrying a British passport); they tend to ask rather detailed and searching questions... Plus the queues are huge, so it takes absolutely ages to clear. Plan for a very long connection...

If you're going to BOG then for goodness sake do try to go up to CTG for a couple of days if you can - it's a magical place and very safe. PM me if you want to know more...