I spent four days in Bogota with minimal -- very minimal -- Spanish language skills. Four years of high school Spanish in the all-too-distant past. There is not a whole lot of English fluency in the hotels and restaurants in Bogota, but ....
(1) The people in Colombia, especially Bogota, have a reputation for speaking the clearest, easiest to understand Spanish out there (including Spain). The reputation is well-deserved. Colombianos speak the TV anchorman version of Spanish. My level of Spanish comprehension was probably triple what it has been compared to listening to Mexican or other South American Spanish speakers.
(2) While English fluency seems to be rare in Bogota, a "good not great" level of English language proficiency is quite common. And the people are extraordinarily friendly and very motivated to improve their English skills. Language will not be a problem, especially if you have basic Spanish language comprehension skills.
Regarding hotels, your budget seems a bit low for a decent hotel in Bogota. Generally Bogota is a bargain. Restaurant food is a great deal. Cabs are cheap and plentiful. But you will probably need to pay $110 to $130 per night for a decent hotel in a good neighborhood. I can't answer your question about which neighborhood best suits you. I don't know enough about you! I heard avoid the La Candelaria and Centro hotels because the streets aren't safe after dark (although perfectly safe during daylight hours). So you probably want to go north of downtown. Do not look south. There are a lot of hotels, restaurants, shopping, nightlife, etc. in the streets numbered in the 90s and low 100s (Calle 92 and above). But, at night, you will taking cabs to go where you want to go. But, as I said, cabs are cheap plentiful.
I did not make it to Cartagena on my trip. I did go to Medellin. I'm a broken record on this point, but I thought Medellin was skip-able. I definitely want to go to Cartagena someday.
As for yoga. Sorry. Can't help you there.
Edited: 7:55 pm, October 17, 2012