Unlike the classic arena, where the following only applies to platinum, in tag team each tier has a limited number of players. It's no problem to stay in bronze.
The only reason to do tag team is to get the free legendary hero, Drexthar. Make sure to buy fragments for him every day, there is a cooldown of 24h for buying them.
In addition to Drexthar there are a number of tag team quests you might try, if you get enough of them you can win a variety of additional prizes. There seems to be little set standard for the opponents you get, all you can try is frequent resets and manage your tokens.
Best to stay in the lowest level, you can still do all the tasks. If you move up the opponents get horrendous.