1. Your brief is not clear as to Jurisdiction other than stating currently you as a proposed petitioner is living in Chennai and proposed respondent wife is currently living in Bangalore.
Section 19 of the Hindu Marriage Act deals with jurisdiction and procedures. Before the amendment made to Section 19 as per Act 50 of 2003, the provision was as under:-
19. Court to which petition shall be presented:- Every petition under this Act shall be presented to the District Court within the local limits of whose ordinary original civil jurisdiction-
(i) the marriage was solemnized, or
(ii) the respondent, at the time of presentation of the petition, resides, or
(iii) the parties to the marriage last resided together, or
[ (iii-a) in case the wife is the petitioner, where she is residing on the date of presentation of the petition, or]
(iv) the petitioner is residing at the time of the presentation of the petition, in a case where the respondent is, at that time, residing outside the territories to which this Act extends, or has not been heard of as being alive for a period of seven years or more by those persons who would naturally have heard of him if he were alive.
2. In my opinion you should file Divorce at Bangalore and not at Chennai if speed is priority.
3. If you want to frustrate her then you can file at Chennai and let her approach SC to get it un-oposed by you transferred to Bangalore whereby you keep tab of Cause List of SC. This way she will spend some money on hiring SC AOR and Chennai / Bangalore are not that far by Shatabdi Train / Bus not to attend case at Bangalore afterall.
4. Clarify here (i) the parties to the marriage last resided together?